2(3x-7)(6x+5)=0

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Solution for 2(3x-7)(6x+5)=0 equation: 


Simplifying
2(3x + -7)(6x + 5) = 0

Reorder the terms:
2(-7 + 3x)(6x + 5) = 0

Reorder the terms:
2(-7 + 3x)(5 + 6x) = 0

Multiply (-7 + 3x) * (5 + 6x)
2(-7(5 + 6x) + 3x * (5 + 6x)) = 0
2((5 * -7 + 6x * -7) + 3x * (5 + 6x)) = 0
2((-35 + -42x) + 3x * (5 + 6x)) = 0
2(-35 + -42x + (5 * 3x + 6x * 3x)) = 0
2(-35 + -42x + (15x + 18x2)) = 0

Combine like terms: -42x + 15x = -27x
2(-35 + -27x + 18x2) = 0
(-35 * 2 + -27x * 2 + 18x2 * 2) = 0
(-70 + -54x + 36x2) = 0

Solving
-70 + -54x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + -27x + 18x2) = 0

Factor a trinomial.
2((-5 + -6x)(7 + -3x)) = 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 '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-0.8333333333, 2.333333333}

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