(-2x+15)(32-4x)=0

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Solution for (-2x+15)(32-4x)=0 equation: 


Simplifying
(-2x + 15)(32 + -4x) = 0

Reorder the terms:
(15 + -2x)(32 + -4x) = 0

Multiply (15 + -2x) * (32 + -4x)
(15(32 + -4x) + -2x * (32 + -4x)) = 0
((32 * 15 + -4x * 15) + -2x * (32 + -4x)) = 0
((480 + -60x) + -2x * (32 + -4x)) = 0
(480 + -60x + (32 * -2x + -4x * -2x)) = 0
(480 + -60x + (-64x + 8x2)) = 0

Combine like terms: -60x + -64x = -124x
(480 + -124x + 8x2) = 0

Solving
480 + -124x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(120 + -31x + 2x2) = 0

Factor a trinomial.
4((15 + -2x)(8 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(15 + -2x)' equal to zero and attempt to solve:

Simplifying
15 + -2x = 0

Solving
15 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-15' to each side of the equation.
15 + -15 + -2x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -2x = 0 + -15
-2x = 0 + -15

Combine like terms: 0 + -15 = -15
-2x = -15

Divide each side by '-2'.
x = 7.5

Simplifying
x = 7.5

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {7.5, 8}

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