# Solve for u -4/3u-5/2=3/2u-6

-43u-52=32u-6
Simplify each term.
Combine u and 43.
-u⋅43-52=32u-6
Move 4 to the left of u.
-4u3-52=32u-6
-4u3-52=32u-6
Combine 32 and u.
-4u3-52=3u2-6
Move all terms containing u to the left side of the equation.
Subtract 3u2 from both sides of the equation.
-4u3-52-3u2=-6
To write -4u3 as a fraction with a common denominator, multiply by 22.
-4u3⋅22-3u2-52=-6
To write -3u2 as a fraction with a common denominator, multiply by 33.
-4u3⋅22-3u2⋅33-52=-6
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
Multiply 4u3 and 22.
-4u⋅23⋅2-3u2⋅33-52=-6
Multiply 3 by 2.
-4u⋅26-3u2⋅33-52=-6
Multiply 3u2 and 33.
-4u⋅26-3u⋅32⋅3-52=-6
Multiply 2 by 3.
-4u⋅26-3u⋅36-52=-6
-4u⋅26-3u⋅36-52=-6
Combine the numerators over the common denominator.
-4u⋅2-3u⋅36-52=-6
Simplify each term.
Simplify the numerator.
Factor u out of -4u⋅2-3u⋅3.
Factor u out of -4u⋅2.
u(-4⋅2)-3u⋅36-52=-6
Factor u out of -3u⋅3.
u(-4⋅2)+u(-3⋅3)6-52=-6
Factor u out of u(-4⋅2)+u(-3⋅3).
u(-4⋅2-3⋅3)6-52=-6
u(-4⋅2-3⋅3)6-52=-6
Multiply -4 by 2.
u(-8-3⋅3)6-52=-6
Multiply -3 by 3.
u(-8-9)6-52=-6
Subtract 9 from -8.
u⋅-176-52=-6
u⋅-176-52=-6
Move -17 to the left of u.
-17⋅u6-52=-6
Move the negative in front of the fraction.
-17u6-52=-6
-17u6-52=-6
-17u6-52=-6
Move all terms not containing u to the right side of the equation.
Add 52 to both sides of the equation.
-17u6=-6+52
To write -6 as a fraction with a common denominator, multiply by 22.
-17u6=-6⋅22+52
Combine -6 and 22.
-17u6=-6⋅22+52
Combine the numerators over the common denominator.
-17u6=-6⋅2+52
Simplify the numerator.
Multiply -6 by 2.
-17u6=-12+52
-17u6=-72
-17u6=-72
Move the negative in front of the fraction.
-17u6=-72
-17u6=-72
Multiply both sides of the equation by -617.
-617⋅(-17u6)=-617⋅(-72)
Simplify both sides of the equation.
Simplify -617⋅(-17u6).
Cancel the common factor of 6.
Move the leading negative in -617 into the numerator.
-617⋅(-17u6)=-617⋅(-72)
Move the leading negative in -17u6 into the numerator.
-617⋅-17u6=-617⋅(-72)
Factor 6 out of -6.
6(-1)17⋅-17u6=-617⋅(-72)
Cancel the common factor.
6⋅-117⋅-17u6=-617⋅(-72)
Rewrite the expression.
-117⋅(-17u)=-617⋅(-72)
-117⋅(-17u)=-617⋅(-72)
Cancel the common factor of 17.
Factor 17 out of -17u.
-117⋅(17(-u))=-617⋅(-72)
Cancel the common factor.
-117⋅(17(-u))=-617⋅(-72)
Rewrite the expression.
-1⋅(-u)=-617⋅(-72)
-1⋅(-u)=-617⋅(-72)
Multiply.
Multiply -1 by -1.
1⋅u=-617⋅(-72)
Multiply u by 1.
u=-617⋅(-72)
u=-617⋅(-72)
u=-617⋅(-72)
Simplify -617⋅(-72).
Cancel the common factor of 2.
Move the leading negative in -617 into the numerator.
u=-617⋅(-72)
Move the leading negative in -72 into the numerator.
u=-617⋅-72
Factor 2 out of -6.
u=2(-3)17⋅-72
Cancel the common factor.
u=2⋅-317⋅-72
Rewrite the expression.
u=-317⋅-7
u=-317⋅-7
Combine -317 and -7.
u=-3⋅-717
Multiply -3 by -7.
u=2117
u=2117
u=2117
The result can be shown in multiple forms.
Exact Form:
u=2117
Decimal Form:
u=1.23529411…
Mixed Number Form:
u=1417
Solve for u -4/3u-5/2=3/2u-6

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