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

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


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

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

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

Multiply (-5 + 7x) * (7 + 6x)
3(-5(7 + 6x) + 7x * (7 + 6x)) = 0
3((7 * -5 + 6x * -5) + 7x * (7 + 6x)) = 0
3((-35 + -30x) + 7x * (7 + 6x)) = 0
3(-35 + -30x + (7 * 7x + 6x * 7x)) = 0
3(-35 + -30x + (49x + 42x2)) = 0

Combine like terms: -30x + 49x = 19x
3(-35 + 19x + 42x2) = 0
(-35 * 3 + 19x * 3 + 42x2 * 3) = 0
(-105 + 57x + 126x2) = 0

Solving
-105 + 57x + 126x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-35 + 19x + 42x2) = 0

Factor a trinomial.
3((-7 + -6x)(5 + -7x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-7 + -6x)' equal to zero and attempt to solve: Simplifying -7 + -6x = 0 Solving -7 + -6x = 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 + -6x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6x = 0 + 7 -6x = 0 + 7 Combine like terms: 0 + 7 = 7 -6x = 7 Divide each side by '-6'. x = -1.166666667 Simplifying x = -1.166666667

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 = {-1.166666667, 0.7142857143}

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