2(6x+9)(2x-10)=0

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Solution for 2(6x+9)(2x-10)=0 equation: 


Simplifying
2(6x + 9)(2x + -10) = 0

Reorder the terms:
2(9 + 6x)(2x + -10) = 0

Reorder the terms:
2(9 + 6x)(-10 + 2x) = 0

Multiply (9 + 6x) * (-10 + 2x)
2(9(-10 + 2x) + 6x * (-10 + 2x)) = 0
2((-10 * 9 + 2x * 9) + 6x * (-10 + 2x)) = 0
2((-90 + 18x) + 6x * (-10 + 2x)) = 0
2(-90 + 18x + (-10 * 6x + 2x * 6x)) = 0
2(-90 + 18x + (-60x + 12x2)) = 0

Combine like terms: 18x + -60x = -42x
2(-90 + -42x + 12x2) = 0
(-90 * 2 + -42x * 2 + 12x2 * 2) = 0
(-180 + -84x + 24x2) = 0

Solving
-180 + -84x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-15 + -7x + 2x2) = 0

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

Ignore the factor 12.

Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-1.5, 5}

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