(6x+12)(5x-15)=0

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Solution for (6x+12)(5x-15)=0 equation: 


Simplifying
(6x + 12)(5x + -15) = 0

Reorder the terms:
(12 + 6x)(5x + -15) = 0

Reorder the terms:
(12 + 6x)(-15 + 5x) = 0

Multiply (12 + 6x) * (-15 + 5x)
(12(-15 + 5x) + 6x * (-15 + 5x)) = 0
((-15 * 12 + 5x * 12) + 6x * (-15 + 5x)) = 0
((-180 + 60x) + 6x * (-15 + 5x)) = 0
(-180 + 60x + (-15 * 6x + 5x * 6x)) = 0
(-180 + 60x + (-90x + 30x2)) = 0

Combine like terms: 60x + -90x = -30x
(-180 + -30x + 30x2) = 0

Solving
-180 + -30x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '30'.
30(-6 + -1x + x2) = 0

Factor a trinomial.
30((-2 + -1x)(3 + -1x)) = 0

Ignore the factor 30.

Subproblem 1
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

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 = {-2, 3}

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