Solve for n 29n^2-160n+256=5n^2

Math
29n2-160n+256=5n2
Move all terms containing n to the left side of the equation.
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Subtract 5n2 from both sides of the equation.
29n2-160n+256-5n2=0
Subtract 5n2 from 29n2.
24n2-160n+256=0
24n2-160n+256=0
Factor the left side of the equation.
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Factor 8 out of 24n2-160n+256.
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Factor 8 out of 24n2.
8(3n2)-160n+256=0
Factor 8 out of -160n.
8(3n2)+8(-20n)+256=0
Factor 8 out of 256.
8(3n2)+8(-20n)+8(32)=0
Factor 8 out of 8(3n2)+8(-20n).
8(3n2-20n)+8(32)=0
Factor 8 out of 8(3n2-20n)+8(32).
8(3n2-20n+32)=0
8(3n2-20n+32)=0
Factor.
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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=3⋅32=96 and whose sum is b=-20.
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Factor -20 out of -20n.
8(3n2-20n+32)=0
Rewrite -20 as -8 plus -12
8(3n2+(-8-12)n+32)=0
Apply the distributive property.
8(3n2-8n-12n+32)=0
8(3n2-8n-12n+32)=0
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
8((3n2-8n)-12n+32)=0
Factor out the greatest common factor (GCF) from each group.
8(n(3n-8)-4(3n-8))=0
8(n(3n-8)-4(3n-8))=0
Factor the polynomial by factoring out the greatest common factor, 3n-8.
8((3n-8)(n-4))=0
8((3n-8)(n-4))=0
Remove unnecessary parentheses.
8(3n-8)(n-4)=0
8(3n-8)(n-4)=0
8(3n-8)(n-4)=0
Divide each term by 8 and simplify.
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Divide each term in 8(3n-8)(n-4)=0 by 8.
8(3n-8)(n-4)8=08
Simplify 8(3n-8)(n-4)8.
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Cancel the common factor of 8.
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Cancel the common factor.
8(3n-8)(n-4)8=08
Divide (3n-8)(n-4) by 1.
(3n-8)(n-4)=08
(3n-8)(n-4)=08
Expand (3n-8)(n-4) using the FOIL Method.
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Apply the distributive property.
3n(n-4)-8(n-4)=08
Apply the distributive property.
3n⋅n+3n⋅-4-8(n-4)=08
Apply the distributive property.
3n⋅n+3n⋅-4-8n-8⋅-4=08
3n⋅n+3n⋅-4-8n-8⋅-4=08
Simplify and combine like terms.
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Simplify each term.
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Multiply n by n by adding the exponents.
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Move n.
3(n⋅n)+3n⋅-4-8n-8⋅-4=08
Multiply n by n.
3n2+3n⋅-4-8n-8⋅-4=08
3n2+3n⋅-4-8n-8⋅-4=08
Multiply -4 by 3.
3n2-12n-8n-8⋅-4=08
Multiply -8 by -4.
3n2-12n-8n+32=08
3n2-12n-8n+32=08
Subtract 8n from -12n.
3n2-20n+32=08
3n2-20n+32=08
3n2-20n+32=08
Divide 0 by 8.
3n2-20n+32=0
3n2-20n+32=0
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=3⋅32=96 and whose sum is b=-20.
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Factor -20 out of -20n.
3n2-20n+32=0
Rewrite -20 as -8 plus -12
3n2+(-8-12)n+32=0
Apply the distributive property.
3n2-8n-12n+32=0
3n2-8n-12n+32=0
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(3n2-8n)-12n+32=0
Factor out the greatest common factor (GCF) from each group.
n(3n-8)-4(3n-8)=0
n(3n-8)-4(3n-8)=0
Factor the polynomial by factoring out the greatest common factor, 3n-8.
(3n-8)(n-4)=0
(3n-8)(n-4)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
3n-8=0
n-4=0
Set the first factor equal to 0 and solve.
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Set the first factor equal to 0.
3n-8=0
Add 8 to both sides of the equation.
3n=8
Divide each term by 3 and simplify.
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Divide each term in 3n=8 by 3.
3n3=83
Cancel the common factor of 3.
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Cancel the common factor.
3n3=83
Divide n by 1.
n=83
n=83
n=83
n=83
Set the next factor equal to 0 and solve.
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Set the next factor equal to 0.
n-4=0
Add 4 to both sides of the equation.
n=4
n=4
The final solution is all the values that make (3n-8)(n-4)=0 true.
n=83,4
The result can be shown in multiple forms.
Exact Form:
n=83,4
Decimal Form:
n=2.6‾,4
Mixed Number Form:
n=223,4
Solve for n 29n^2-160n+256=5n^2

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