(5x+15)(12-3x)=0

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Solution for (5x+15)(12-3x)=0 equation: 


Simplifying
(5x + 15)(12 + -3x) = 0

Reorder the terms:
(15 + 5x)(12 + -3x) = 0

Multiply (15 + 5x) * (12 + -3x)
(15(12 + -3x) + 5x * (12 + -3x)) = 0
((12 * 15 + -3x * 15) + 5x * (12 + -3x)) = 0
((180 + -45x) + 5x * (12 + -3x)) = 0
(180 + -45x + (12 * 5x + -3x * 5x)) = 0
(180 + -45x + (60x + -15x2)) = 0

Combine like terms: -45x + 60x = 15x
(180 + 15x + -15x2) = 0

Solving
180 + 15x + -15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15'.
15(12 + x + -1x2) = 0

Factor a trinomial.
15((4 + -1x)(3 + x)) = 0

Ignore the factor 15.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
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
Solution
x = {4, -3}

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