12-2(x+3)=x-4x(2-x)

Solution for 12-2(x+3)=x-4x(2-x) equation:

Simplifying
12 + -2(x + 3) = x + -4x(2 + -1x)

Reorder the terms:
12 + -2(3 + x) = x + -4x(2 + -1x)
12 + (3 * -2 + x * -2) = x + -4x(2 + -1x)
12 + (-6 + -2x) = x + -4x(2 + -1x)

Combine like terms: 12 + -6 = 6
6 + -2x = x + -4x(2 + -1x)
6 + -2x = x + (2 * -4x + -1x * -4x)
6 + -2x = x + (-8x + 4x2)

Combine like terms: x + -8x = -7x
6 + -2x = -7x + 4x2

Solving
6 + -2x = -7x + 4x2

Solving for variable 'x'.

Combine like terms: -2x + 7x = 5x
6 + 5x + -4x2 = -7x + 4x2 + 7x + -4x2

Reorder the terms:
6 + 5x + -4x2 = -7x + 7x + 4x2 + -4x2

Combine like terms: -7x + 7x = 0
6 + 5x + -4x2 = 0 + 4x2 + -4x2
6 + 5x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
6 + 5x + -4x2 = 0

Factor a trinomial.
(2 + -1x)(3 + 4x) = 0

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 '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4x = 0 + -3

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

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

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75
Solution
x = {2, -0.75}