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

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


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

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

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

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

Combine like terms: -30x + 35x = 5x
2(-25 + 5x + 42x2) = 0
(-25 * 2 + 5x * 2 + 42x2 * 2) = 0
(-50 + 10x + 84x2) = 0

Solving
-50 + 10x + 84x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 5x + 42x2) = 0

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

Ignore the factor 2.

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

Simplifying
-5 + -6x = 0

Solving
-5 + -6x = 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 + -6x = 0 + 5

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

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

Divide each side by '-6'.
x = -0.8333333333

Simplifying
x = -0.8333333333

Subproblem 2
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
Solution
x = {-0.8333333333, 0.7142857143}

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