(2x-6)(5x+5)=0

Solution for (2x-6)(5x+5)=0 equation:

Simplifying
(2x + -6)(5x + 5) = 0

Reorder the terms:
(-6 + 2x)(5x + 5) = 0

Reorder the terms:
(-6 + 2x)(5 + 5x) = 0

Multiply (-6 + 2x) * (5 + 5x)
(-6(5 + 5x) + 2x * (5 + 5x)) = 0
((5 * -6 + 5x * -6) + 2x * (5 + 5x)) = 0
((-30 + -30x) + 2x * (5 + 5x)) = 0
(-30 + -30x + (5 * 2x + 5x * 2x)) = 0
(-30 + -30x + (10x + 10x2)) = 0

Combine like terms: -30x + 10x = -20x
(-30 + -20x + 10x2) = 0

Solving
-30 + -20x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-3 + -2x + x2) = 0

Factor a trinomial.
10((-1 + -1x)(3 + -1x)) = 0

Ignore the factor 10.
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 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1, 3}