(4x+4)(2x-3)=0

Solution for (4x+4)(2x-3)=0 equation:

Simplifying
(4x + 4)(2x + -3) = 0

Reorder the terms:
(4 + 4x)(2x + -3) = 0

Reorder the terms:
(4 + 4x)(-3 + 2x) = 0

Multiply (4 + 4x) * (-3 + 2x)
(4(-3 + 2x) + 4x * (-3 + 2x)) = 0
((-3 * 4 + 2x * 4) + 4x * (-3 + 2x)) = 0
((-12 + 8x) + 4x * (-3 + 2x)) = 0
(-12 + 8x + (-3 * 4x + 2x * 4x)) = 0
(-12 + 8x + (-12x + 8x2)) = 0

Combine like terms: 8x + -12x = -4x
(-12 + -4x + 8x2) = 0

Solving
-12 + -4x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + -1x + 2x2) = 0

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

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

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

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1, 1.5}