(2x-6)(5x+12)=0

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Solution for (2x-6)(5x+12)=0 equation: 


Simplifying
(2x + -6)(5x + 12) = 0

Reorder the terms:
(-6 + 2x)(5x + 12) = 0

Reorder the terms:
(-6 + 2x)(12 + 5x) = 0

Multiply (-6 + 2x) * (12 + 5x)
(-6(12 + 5x) + 2x * (12 + 5x)) = 0
((12 * -6 + 5x * -6) + 2x * (12 + 5x)) = 0
((-72 + -30x) + 2x * (12 + 5x)) = 0
(-72 + -30x + (12 * 2x + 5x * 2x)) = 0
(-72 + -30x + (24x + 10x2)) = 0

Combine like terms: -30x + 24x = -6x
(-72 + -6x + 10x2) = 0

Solving
-72 + -6x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + -3x + 5x2) = 0

Factor a trinomial.
2((-12 + -5x)(3 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + -5x)' equal to zero and attempt to solve:

Simplifying
-12 + -5x = 0

Solving
-12 + -5x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -5x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -5x = 0 + 12
-5x = 0 + 12

Combine like terms: 0 + 12 = 12
-5x = 12

Divide each side by '-5'.
x = -2.4

Simplifying
x = -2.4

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 = {-2.4, 3}

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