(2x)(8-x)=(x^2-12)

Solution for (2x)(8-x)=(x^2-12) equation:

Simplifying
(2x)(8 + -1x) = (x2 + -12)

Remove parenthesis around (2x)
2x(8 + -1x) = (x2 + -12)
(8 * 2x + -1x * 2x) = (x2 + -12)
(16x + -2x2) = (x2 + -12)

Reorder the terms:
16x + -2x2 = (-12 + x2)

Remove parenthesis around (-12 + x2)
16x + -2x2 = -12 + x2

Solving
16x + -2x2 = -12 + x2

Solving for variable 'x'.

Reorder the terms:
12 + 16x + -2x2 + -1x2 = -12 + x2 + 12 + -1x2

Combine like terms: -2x2 + -1x2 = -3x2
12 + 16x + -3x2 = -12 + x2 + 12 + -1x2

Reorder the terms:
12 + 16x + -3x2 = -12 + 12 + x2 + -1x2

Combine like terms: -12 + 12 = 0
12 + 16x + -3x2 = 0 + x2 + -1x2
12 + 16x + -3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + 16x + -3x2 = 0

Factor a trinomial.
(6 + -1x)(2 + 3x) = 0

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {6, -0.6666666667}