(2x-2)(3x+15)=0

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Solution for (2x-2)(3x+15)=0 equation: 


Simplifying
(2x + -2)(3x + 15) = 0

Reorder the terms:
(-2 + 2x)(3x + 15) = 0

Reorder the terms:
(-2 + 2x)(15 + 3x) = 0

Multiply (-2 + 2x) * (15 + 3x)
(-2(15 + 3x) + 2x * (15 + 3x)) = 0
((15 * -2 + 3x * -2) + 2x * (15 + 3x)) = 0
((-30 + -6x) + 2x * (15 + 3x)) = 0
(-30 + -6x + (15 * 2x + 3x * 2x)) = 0
(-30 + -6x + (30x + 6x2)) = 0

Combine like terms: -6x + 30x = 24x
(-30 + 24x + 6x2) = 0

Solving
-30 + 24x + 6x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 6.

Subproblem 1
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

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 = {-5, 1}

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