(x-5)(3x+3)=0

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

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

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

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

Multiply (-5 + x) * (3 + 3x)
(-5(3 + 3x) + x(3 + 3x)) = 0
((3 * -5 + 3x * -5) + x(3 + 3x)) = 0
((-15 + -15x) + x(3 + 3x)) = 0
(-15 + -15x + (3 * x + 3x * x)) = 0
(-15 + -15x + (3x + 3x2)) = 0

Combine like terms: -15x + 3x = -12x
(-15 + -12x + 3x2) = 0

Solving
-15 + -12x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -4x + x2) = 0

Factor a trinomial.
3((-1 + -1x)(5 + -1x)) = 0

Ignore the factor 3.
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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-1, 5}