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

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


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

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

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

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

Combine like terms: 60x + -30x = 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((-4 + -1x)(2 + -1x)) = 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 '(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
Solution
x = {-4, 2}

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