(-4x-8)(-5x+12)=0

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Solution for (-4x-8)(-5x+12)=0 equation: 


Simplifying
(-4x + -8)(-5x + 12) = 0

Reorder the terms:
(-8 + -4x)(-5x + 12) = 0

Reorder the terms:
(-8 + -4x)(12 + -5x) = 0

Multiply (-8 + -4x) * (12 + -5x)
(-8(12 + -5x) + -4x * (12 + -5x)) = 0
((12 * -8 + -5x * -8) + -4x * (12 + -5x)) = 0
((-96 + 40x) + -4x * (12 + -5x)) = 0
(-96 + 40x + (12 * -4x + -5x * -4x)) = 0
(-96 + 40x + (-48x + 20x2)) = 0

Combine like terms: 40x + -48x = -8x
(-96 + -8x + 20x2) = 0

Solving
-96 + -8x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-24 + -2x + 5x2) = 0

Factor a trinomial.
4((-2 + -1x)(12 + -5x)) = 0

Ignore the factor 4.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(12 + -5x)' equal to zero and attempt to solve:

Simplifying
12 + -5x = 0

Solving
12 + -5x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -5x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -5x = 0 + -12
-5x = 0 + -12

Combine like terms: 0 + -12 = -12
-5x = -12

Divide each side by '-5'.
x = 2.4

Simplifying
x = 2.4
Solution
x = {-2, 2.4}

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