(2x+12)(7x-5)=0

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Solution for (2x+12)(7x-5)=0 equation: 


Simplifying
(2x + 12)(7x + -5) = 0

Reorder the terms:
(12 + 2x)(7x + -5) = 0

Reorder the terms:
(12 + 2x)(-5 + 7x) = 0

Multiply (12 + 2x) * (-5 + 7x)
(12(-5 + 7x) + 2x * (-5 + 7x)) = 0
((-5 * 12 + 7x * 12) + 2x * (-5 + 7x)) = 0
((-60 + 84x) + 2x * (-5 + 7x)) = 0
(-60 + 84x + (-5 * 2x + 7x * 2x)) = 0
(-60 + 84x + (-10x + 14x2)) = 0

Combine like terms: 84x + -10x = 74x
(-60 + 74x + 14x2) = 0

Solving
-60 + 74x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + 37x + 7x2) = 0

Factor a trinomial.
2((-6 + -1x)(5 + -7x)) = 0

Ignore the factor 2.

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

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

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 = {-6, 0.7142857143}

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