(5x-10)(2x+6)=0

Solution for (5x-10)(2x+6)=0 equation:

Simplifying
(5x + -10)(2x + 6) = 0

Reorder the terms:
(-10 + 5x)(2x + 6) = 0

Reorder the terms:
(-10 + 5x)(6 + 2x) = 0

Multiply (-10 + 5x) * (6 + 2x)
(-10(6 + 2x) + 5x * (6 + 2x)) = 0
((6 * -10 + 2x * -10) + 5x * (6 + 2x)) = 0
((-60 + -20x) + 5x * (6 + 2x)) = 0
(-60 + -20x + (6 * 5x + 2x * 5x)) = 0
(-60 + -20x + (30x + 10x2)) = 0

Combine like terms: -20x + 30x = 10x
(-60 + 10x + 10x2) = 0

Solving
-60 + 10x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-6 + x + x2) = 0

Factor a trinomial.
10((-3 + -1x)(2 + -1x)) = 0

Ignore the factor 10.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3, 2}