(2x-6)(3x+15)=0

Solution for (2x-6)(3x+15)=0 equation:

Simplifying
(2x + -6)(3x + 15) = 0

Reorder the terms:
(-6 + 2x)(3x + 15) = 0

Reorder the terms:
(-6 + 2x)(15 + 3x) = 0

Multiply (-6 + 2x) * (15 + 3x)
(-6(15 + 3x) + 2x * (15 + 3x)) = 0
((15 * -6 + 3x * -6) + 2x * (15 + 3x)) = 0
((-90 + -18x) + 2x * (15 + 3x)) = 0
(-90 + -18x + (15 * 2x + 3x * 2x)) = 0
(-90 + -18x + (30x + 6x2)) = 0

Combine like terms: -18x + 30x = 12x
(-90 + 12x + 6x2) = 0

Solving
-90 + 12x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-15 + 2x + x2) = 0

Factor a trinomial.
6((-5 + -1x)(3 + -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 '(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 = {-5, 3}