(5x+10)(4x-12)=0

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Solution for (5x+10)(4x-12)=0 equation: 


Simplifying
(5x + 10)(4x + -12) = 0

Reorder the terms:
(10 + 5x)(4x + -12) = 0

Reorder the terms:
(10 + 5x)(-12 + 4x) = 0

Multiply (10 + 5x) * (-12 + 4x)
(10(-12 + 4x) + 5x * (-12 + 4x)) = 0
((-12 * 10 + 4x * 10) + 5x * (-12 + 4x)) = 0
((-120 + 40x) + 5x * (-12 + 4x)) = 0
(-120 + 40x + (-12 * 5x + 4x * 5x)) = 0
(-120 + 40x + (-60x + 20x2)) = 0

Combine like terms: 40x + -60x = -20x
(-120 + -20x + 20x2) = 0

Solving
-120 + -20x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '20'.
20(-6 + -1x + x2) = 0

Factor a trinomial.
20((-2 + -1x)(3 + -1x)) = 0

Ignore the factor 20.

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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