Solve for b (6b-12)/(8b^2+29b+15)=1/(8b+5)+1/(8b^2+29b+15)

Math
6b-128b2+29b+15=18b+5+18b2+29b+15
Factor each term.
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Factor 6 out of 6b-12.
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Factor 6 out of 6b.
6(b)-128b2+29b+15=18b+5+18b2+29b+15
Factor 6 out of -12.
6b+6⋅-28b2+29b+15=18b+5+18b2+29b+15
Factor 6 out of 6b+6⋅-2.
6(b-2)8b2+29b+15=18b+5+18b2+29b+15
6(b-2)8b2+29b+15=18b+5+18b2+29b+15
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=8⋅15=120 and whose sum is b=29.
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Factor 29 out of 29b.
6(b-2)8b2+29(b)+15=18b+5+18b2+29b+15
Rewrite 29 as 5 plus 24
6(b-2)8b2+(5+24)b+15=18b+5+18b2+29b+15
Apply the distributive property.
6(b-2)8b2+5b+24b+15=18b+5+18b2+29b+15
6(b-2)8b2+5b+24b+15=18b+5+18b2+29b+15
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
6(b-2)(8b2+5b)+24b+15=18b+5+18b2+29b+15
Factor out the greatest common factor (GCF) from each group.
6(b-2)b(8b+5)+3(8b+5)=18b+5+18b2+29b+15
6(b-2)b(8b+5)+3(8b+5)=18b+5+18b2+29b+15
Factor the polynomial by factoring out the greatest common factor, 8b+5.
6(b-2)(8b+5)(b+3)=18b+5+18b2+29b+15
6(b-2)(8b+5)(b+3)=18b+5+18b2+29b+15
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=8⋅15=120 and whose sum is b=29.
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Factor 29 out of 29b.
6(b-2)(8b+5)(b+3)=18b+5+18b2+29(b)+15
Rewrite 29 as 5 plus 24
6(b-2)(8b+5)(b+3)=18b+5+18b2+(5+24)b+15
Apply the distributive property.
6(b-2)(8b+5)(b+3)=18b+5+18b2+5b+24b+15
6(b-2)(8b+5)(b+3)=18b+5+18b2+5b+24b+15
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
6(b-2)(8b+5)(b+3)=18b+5+1(8b2+5b)+24b+15
Factor out the greatest common factor (GCF) from each group.
6(b-2)(8b+5)(b+3)=18b+5+1b(8b+5)+3(8b+5)
6(b-2)(8b+5)(b+3)=18b+5+1b(8b+5)+3(8b+5)
Factor the polynomial by factoring out the greatest common factor, 8b+5.
6(b-2)(8b+5)(b+3)=18b+5+1(8b+5)(b+3)
6(b-2)(8b+5)(b+3)=18b+5+1(8b+5)(b+3)
6(b-2)(8b+5)(b+3)=18b+5+1(8b+5)(b+3)
Find the LCD of the terms in the equation.
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Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
(8b+5)(b+3),8b+5,(8b+5)(b+3)
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
The number 1 is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of 1,1,1 is the result of multiplying all prime factors the greatest number of times they occur in either number.
1
The factor for 8b+5 is 8b+5 itself.
(8b+5)=8b+5
(8b+5) occurs 1 time.
The factor for b+3 is b+3 itself.
(b+3)=b+3
(b+3) occurs 1 time.
The factor for 8b+5 is 8b+5 itself.
(8b+5)=8b+5
(8b+5) occurs 1 time.
The factor for b+3 is b+3 itself.
(b+3)=b+3
(b+3) occurs 1 time.
The LCM of 8b+5,b+3,8b+5,8b+5,b+3 is the result of multiplying all factors the greatest number of times they occur in either term.
(8b+5)(b+3)
(8b+5)(b+3)
Multiply each term by (8b+5)(b+3) and simplify.
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Multiply each term in 6(b-2)(8b+5)(b+3)=18b+5+1(8b+5)(b+3) by (8b+5)(b+3) in order to remove all the denominators from the equation.
6(b-2)(8b+5)(b+3)⋅((8b+5)(b+3))=18b+5⋅((8b+5)(b+3))+1(8b+5)(b+3)⋅((8b+5)(b+3))
Simplify 6(b-2)(8b+5)(b+3)⋅((8b+5)(b+3)).
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Cancel the common factor of (8b+5)(b+3).
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Cancel the common factor.
6(b-2)(8b+5)(b+3)⋅((8b+5)(b+3))=18b+5⋅((8b+5)(b+3))+1(8b+5)(b+3)⋅((8b+5)(b+3))
Rewrite the expression.
6(b-2)=18b+5⋅((8b+5)(b+3))+1(8b+5)(b+3)⋅((8b+5)(b+3))
6(b-2)=18b+5⋅((8b+5)(b+3))+1(8b+5)(b+3)⋅((8b+5)(b+3))
Apply the distributive property.
6b+6⋅-2=18b+5⋅((8b+5)(b+3))+1(8b+5)(b+3)⋅((8b+5)(b+3))
Multiply 6 by -2.
6b-12=18b+5⋅((8b+5)(b+3))+1(8b+5)(b+3)⋅((8b+5)(b+3))
6b-12=18b+5⋅((8b+5)(b+3))+1(8b+5)(b+3)⋅((8b+5)(b+3))
Simplify 18b+5⋅((8b+5)(b+3))+1(8b+5)(b+3)⋅((8b+5)(b+3)).
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Simplify each term.
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Cancel the common factor of 8b+5.
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Cancel the common factor.
6b-12=18b+5⋅((8b+5)(b+3))+1(8b+5)(b+3)⋅((8b+5)(b+3))
Rewrite the expression.
6b-12=b+3+1(8b+5)(b+3)⋅((8b+5)(b+3))
6b-12=b+3+1(8b+5)(b+3)⋅((8b+5)(b+3))
Cancel the common factor of (8b+5)(b+3).
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Cancel the common factor.
6b-12=b+3+1(8b+5)(b+3)⋅((8b+5)(b+3))
Rewrite the expression.
6b-12=b+3+1
6b-12=b+3+1
6b-12=b+3+1
Add 3 and 1.
6b-12=b+4
6b-12=b+4
6b-12=b+4
Solve the equation.
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Move all terms containing b to the left side of the equation.
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Subtract b from both sides of the equation.
6b-12-b=4
Subtract b from 6b.
5b-12=4
5b-12=4
Move all terms not containing b to the right side of the equation.
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Add 12 to both sides of the equation.
5b=4+12
Add 4 and 12.
5b=16
5b=16
Divide each term by 5 and simplify.
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Divide each term in 5b=16 by 5.
5b5=165
Cancel the common factor of 5.
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Cancel the common factor.
5b5=165
Divide b by 1.
b=165
b=165
b=165
b=165
The result can be shown in multiple forms.
Exact Form:
b=165
Decimal Form:
b=3.2
Mixed Number Form:
b=315
Solve for b (6b-12)/(8b^2+29b+15)=1/(8b+5)+1/(8b^2+29b+15)

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