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

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

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

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

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

Multiply (2 + 4x) * (-3 + 3x)
(2(-3 + 3x) + 4x * (-3 + 3x)) = 0
((-3 * 2 + 3x * 2) + 4x * (-3 + 3x)) = 0
((-6 + 6x) + 4x * (-3 + 3x)) = 0
(-6 + 6x + (-3 * 4x + 3x * 4x)) = 0
(-6 + 6x + (-12x + 12x2)) = 0

Combine like terms: 6x + -12x = -6x
(-6 + -6x + 12x2) = 0

Solving
-6 + -6x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + -1x + 2x2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
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 = {-0.5, 1}