(6x-3)(4x+4)=0

Solution for (6x-3)(4x+4)=0 equation:

Simplifying
(6x + -3)(4x + 4) = 0

Reorder the terms:
(-3 + 6x)(4x + 4) = 0

Reorder the terms:
(-3 + 6x)(4 + 4x) = 0

Multiply (-3 + 6x) * (4 + 4x)
(-3(4 + 4x) + 6x * (4 + 4x)) = 0
((4 * -3 + 4x * -3) + 6x * (4 + 4x)) = 0
((-12 + -12x) + 6x * (4 + 4x)) = 0
(-12 + -12x + (4 * 6x + 4x * 6x)) = 0
(-12 + -12x + (24x + 24x2)) = 0

Combine like terms: -12x + 24x = 12x
(-12 + 12x + 24x2) = 0

Solving
-12 + 12x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-1 + x + 2x2) = 0

Factor a trinomial.
12((-1 + -1x)(1 + -2x)) = 0

Ignore the factor 12.
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 '(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
Solution
x = {-1, 0.5}