0=(5x+12)(8x-32)

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Solution for 0=(5x+12)(8x-32) equation: 


Simplifying
0 = (5x + 12)(8x + -32)

Reorder the terms:
0 = (12 + 5x)(8x + -32)

Reorder the terms:
0 = (12 + 5x)(-32 + 8x)

Multiply (12 + 5x) * (-32 + 8x)
0 = (12(-32 + 8x) + 5x * (-32 + 8x))
0 = ((-32 * 12 + 8x * 12) + 5x * (-32 + 8x))
0 = ((-384 + 96x) + 5x * (-32 + 8x))
0 = (-384 + 96x + (-32 * 5x + 8x * 5x))
0 = (-384 + 96x + (-160x + 40x2))

Combine like terms: 96x + -160x = -64x
0 = (-384 + -64x + 40x2)

Solving
0 = -384 + -64x + 40x2

Solving for variable 'x'.

Combine like terms: 0 + 384 = 384
384 + 64x + -40x2 = -384 + -64x + 40x2 + 384 + 64x + -40x2

Reorder the terms:
384 + 64x + -40x2 = -384 + 384 + -64x + 64x + 40x2 + -40x2

Combine like terms: -384 + 384 = 0
384 + 64x + -40x2 = 0 + -64x + 64x + 40x2 + -40x2
384 + 64x + -40x2 = -64x + 64x + 40x2 + -40x2

Combine like terms: -64x + 64x = 0
384 + 64x + -40x2 = 0 + 40x2 + -40x2
384 + 64x + -40x2 = 40x2 + -40x2

Combine like terms: 40x2 + -40x2 = 0
384 + 64x + -40x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(48 + 8x + -5x2) = 0

Factor a trinomial.
8((4 + -1x)(12 + 5x)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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 = {4, -2.4}

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