(5x+8)(12-12x)=0

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Solution for (5x+8)(12-12x)=0 equation: 


Simplifying
(5x + 8)(12 + -12x) = 0

Reorder the terms:
(8 + 5x)(12 + -12x) = 0

Multiply (8 + 5x) * (12 + -12x)
(8(12 + -12x) + 5x * (12 + -12x)) = 0
((12 * 8 + -12x * 8) + 5x * (12 + -12x)) = 0
((96 + -96x) + 5x * (12 + -12x)) = 0
(96 + -96x + (12 * 5x + -12x * 5x)) = 0
(96 + -96x + (60x + -60x2)) = 0

Combine like terms: -96x + 60x = -36x
(96 + -36x + -60x2) = 0

Solving
96 + -36x + -60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(8 + -3x + -5x2) = 0

Factor a trinomial.
12((1 + -1x)(8 + 5x)) = 0

Ignore the factor 12.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(8 + 5x)' equal to zero and attempt to solve:

Simplifying
8 + 5x = 0

Solving
8 + 5x = 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 + 5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5x = 0 + -8
5x = 0 + -8

Combine like terms: 0 + -8 = -8
5x = -8

Divide each side by '5'.
x = -1.6

Simplifying
x = -1.6
Solution
x = {1, -1.6}

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