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

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

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

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

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

Multiply (-5 + 3x) * (6 + 5x)
2(-5(6 + 5x) + 3x * (6 + 5x)) = 0
2((6 * -5 + 5x * -5) + 3x * (6 + 5x)) = 0
2((-30 + -25x) + 3x * (6 + 5x)) = 0
2(-30 + -25x + (6 * 3x + 5x * 3x)) = 0
2(-30 + -25x + (18x + 15x2)) = 0

Combine like terms: -25x + 18x = -7x
2(-30 + -7x + 15x2) = 0
(-30 * 2 + -7x * 2 + 15x2 * 2) = 0
(-60 + -14x + 30x2) = 0

Solving
-60 + -14x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + -7x + 15x2) = 0

Factor a trinomial.
2((-6 + -5x)(5 + -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 '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-1.2, 1.666666667}