=(12x+16)(x-12)

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Solution for =(12x+16)(x-12) equation: 


Simplifying
0 = (12x + 16)(x + -12)

Reorder the terms:
0 = (16 + 12x)(x + -12)

Reorder the terms:
0 = (16 + 12x)(-12 + x)

Multiply (16 + 12x) * (-12 + x)
0 = (16(-12 + x) + 12x * (-12 + x))
0 = ((-12 * 16 + x * 16) + 12x * (-12 + x))
0 = ((-192 + 16x) + 12x * (-12 + x))
0 = (-192 + 16x + (-12 * 12x + x * 12x))
0 = (-192 + 16x + (-144x + 12x2))

Combine like terms: 16x + -144x = -128x
0 = (-192 + -128x + 12x2)

Solving
0 = -192 + -128x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + 192 = 192
192 + 128x + -12x2 = -192 + -128x + 12x2 + 192 + 128x + -12x2

Reorder the terms:
192 + 128x + -12x2 = -192 + 192 + -128x + 128x + 12x2 + -12x2

Combine like terms: -192 + 192 = 0
192 + 128x + -12x2 = 0 + -128x + 128x + 12x2 + -12x2
192 + 128x + -12x2 = -128x + 128x + 12x2 + -12x2

Combine like terms: -128x + 128x = 0
192 + 128x + -12x2 = 0 + 12x2 + -12x2
192 + 128x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
192 + 128x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(48 + 32x + -3x2) = 0

Factor a trinomial.
4((12 + -1x)(4 + 3x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 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 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12

Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 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 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333
Solution
x = {12, -1.333333333}

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