4x(x-4)=12x+72

Solution for 4x(x-4)=12x+72 equation:

Simplifying
4x(x + -4) = 12x + 72

Reorder the terms:
4x(-4 + x) = 12x + 72
(-4 * 4x + x * 4x) = 12x + 72
(-16x + 4x2) = 12x + 72

Reorder the terms:
-16x + 4x2 = 72 + 12x

Solving
-16x + 4x2 = 72 + 12x

Solving for variable 'x'.

Reorder the terms:
-72 + -16x + -12x + 4x2 = 72 + 12x + -72 + -12x

Combine like terms: -16x + -12x = -28x
-72 + -28x + 4x2 = 72 + 12x + -72 + -12x

Reorder the terms:
-72 + -28x + 4x2 = 72 + -72 + 12x + -12x

Combine like terms: 72 + -72 = 0
-72 + -28x + 4x2 = 0 + 12x + -12x
-72 + -28x + 4x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-72 + -28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + -7x + x2) = 0

Factor a trinomial.
4((-2 + -1x)(9 + -1x)) = 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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-2, 9}