2(3x-2)(5x+6)=0

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Solution for 2(3x-2)(5x+6)=0 equation: 


Simplifying
2(3x + -2)(5x + 6) = 0

Reorder the terms:
2(-2 + 3x)(5x + 6) = 0

Reorder the terms:
2(-2 + 3x)(6 + 5x) = 0

Multiply (-2 + 3x) * (6 + 5x)
2(-2(6 + 5x) + 3x * (6 + 5x)) = 0
2((6 * -2 + 5x * -2) + 3x * (6 + 5x)) = 0
2((-12 + -10x) + 3x * (6 + 5x)) = 0
2(-12 + -10x + (6 * 3x + 5x * 3x)) = 0
2(-12 + -10x + (18x + 15x2)) = 0

Combine like terms: -10x + 18x = 8x
2(-12 + 8x + 15x2) = 0
(-12 * 2 + 8x * 2 + 15x2 * 2) = 0
(-24 + 16x + 30x2) = 0

Solving
-24 + 16x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 8x + 15x2) = 0

Factor a trinomial.
2((-6 + -5x)(2 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-6 + -5x)' equal to zero and attempt to solve:

Simplifying
-6 + -5x = 0

Solving
-6 + -5x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5x = 0 + 6
-5x = 0 + 6

Combine like terms: 0 + 6 = 6
-5x = 6

Divide each side by '-5'.
x = -1.2

Simplifying
x = -1.2

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

Simplifying
2 + -3x = 0

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

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-1.2, 0.6666666667}

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