(4x-1)*(2x+2)=12

Solution for (4x-1)*(2x+2)=12 equation:

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

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

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

Multiply (-1 + 4x) * (2 + 2x)
(-1(2 + 2x) + 4x * (2 + 2x)) = 12
((2 * -1 + 2x * -1) + 4x * (2 + 2x)) = 12
((-2 + -2x) + 4x * (2 + 2x)) = 12
(-2 + -2x + (2 * 4x + 2x * 4x)) = 12
(-2 + -2x + (8x + 8x2)) = 12

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

Solving
-2 + 6x + 8x2 = 12

Solving for variable 'x'.

Reorder the terms:
-2 + -12 + 6x + 8x2 = 12 + -12

Combine like terms: -2 + -12 = -14
-14 + 6x + 8x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-14 + 6x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 3x + 4x2) = 0

Factor a trinomial.
2((-7 + -4x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -4x)' equal to zero and attempt to solve:

Simplifying
-7 + -4x = 0

Solving
-7 + -4x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -4x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -4x = 0 + 7
-4x = 0 + 7

Combine like terms: 0 + 7 = 7
-4x = 7

Divide each side by '-4'.
x = -1.75

Simplifying
x = -1.75
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-1.75, 1}