2(5x-6)(7x+5)=0

Solution for 2(5x-6)(7x+5)=0 equation:

Simplifying
2(5x + -6)(7x + 5) = 0

Reorder the terms:
2(-6 + 5x)(7x + 5) = 0

Reorder the terms:
2(-6 + 5x)(5 + 7x) = 0

Multiply (-6 + 5x) * (5 + 7x)
2(-6(5 + 7x) + 5x * (5 + 7x)) = 0
2((5 * -6 + 7x * -6) + 5x * (5 + 7x)) = 0
2((-30 + -42x) + 5x * (5 + 7x)) = 0
2(-30 + -42x + (5 * 5x + 7x * 5x)) = 0
2(-30 + -42x + (25x + 35x2)) = 0

Combine like terms: -42x + 25x = -17x
2(-30 + -17x + 35x2) = 0
(-30 * 2 + -17x * 2 + 35x2 * 2) = 0
(-60 + -34x + 70x2) = 0

Solving
-60 + -34x + 70x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + -17x + 35x2) = 0

Factor a trinomial.
2((-5 + -7x)(6 + -5x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -7x)' equal to zero and attempt to solve:

Simplifying
-5 + -7x = 0

Solving
-5 + -7x = 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 + -7x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -7x = 0 + 5
-7x = 0 + 5

Combine like terms: 0 + 5 = 5
-7x = 5

Divide each side by '-7'.
x = -0.7142857143

Simplifying
x = -0.7142857143
Subproblem 2
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
Solution
x = {-0.7142857143, 1.2}