-5(x-3)(2x-6)=0

Solution for -5(x-3)(2x-6)=0 equation:

Simplifying
-5(x + -3)(2x + -6) = 0

Reorder the terms:
-5(-3 + x)(2x + -6) = 0

Reorder the terms:
-5(-3 + x)(-6 + 2x) = 0

Multiply (-3 + x) * (-6 + 2x)
-5(-3(-6 + 2x) + x(-6 + 2x)) = 0
-5((-6 * -3 + 2x * -3) + x(-6 + 2x)) = 0
-5((18 + -6x) + x(-6 + 2x)) = 0
-5(18 + -6x + (-6 * x + 2x * x)) = 0
-5(18 + -6x + (-6x + 2x2)) = 0

Combine like terms: -6x + -6x = -12x
-5(18 + -12x + 2x2) = 0
(18 * -5 + -12x * -5 + 2x2 * -5) = 0
(-90 + 60x + -10x2) = 0

Solving
-90 + 60x + -10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-9 + 6x + -1x2) = 0

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

Ignore the factor 10.
Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

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

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

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

Simplifying
x = 3
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 = {3, 3}