(5x+10)(3x-12)=0

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Solution for (5x+10)(3x-12)=0 equation: 


Simplifying
(5x + 10)(3x + -12) = 0

Reorder the terms:
(10 + 5x)(3x + -12) = 0

Reorder the terms:
(10 + 5x)(-12 + 3x) = 0

Multiply (10 + 5x) * (-12 + 3x)
(10(-12 + 3x) + 5x * (-12 + 3x)) = 0
((-12 * 10 + 3x * 10) + 5x * (-12 + 3x)) = 0
((-120 + 30x) + 5x * (-12 + 3x)) = 0
(-120 + 30x + (-12 * 5x + 3x * 5x)) = 0
(-120 + 30x + (-60x + 15x2)) = 0

Combine like terms: 30x + -60x = -30x
(-120 + -30x + 15x2) = 0

Solving
-120 + -30x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15'.
15(-8 + -2x + x2) = 0

Factor a trinomial.
15((-2 + -1x)(4 + -1x)) = 0

Ignore the factor 15.

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 '(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
Solution
x = {-2, 4}

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