(4x-4)(5x+6)=0

Solution for (4x-4)(5x+6)=0 equation:

Simplifying
(4x + -4)(5x + 6) = 0

Reorder the terms:
(-4 + 4x)(5x + 6) = 0

Reorder the terms:
(-4 + 4x)(6 + 5x) = 0

Multiply (-4 + 4x) * (6 + 5x)
(-4(6 + 5x) + 4x * (6 + 5x)) = 0
((6 * -4 + 5x * -4) + 4x * (6 + 5x)) = 0
((-24 + -20x) + 4x * (6 + 5x)) = 0
(-24 + -20x + (6 * 4x + 5x * 4x)) = 0
(-24 + -20x + (24x + 20x2)) = 0

Combine like terms: -20x + 24x = 4x
(-24 + 4x + 20x2) = 0

Solving
-24 + 4x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + x + 5x2) = 0

Factor a trinomial.
4((-6 + -5x)(1 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-6 + -5x)' equal to zero and attempt to solve:

Simplifying
-6 + -5x = 0

Solving
-6 + -5x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5x = 0 + 6

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

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

Divide each side by '-5'.
x = -1.2

Simplifying
x = -1.2
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 = {-1.2, 1}