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

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


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

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

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

Multiply (12 + 2x) * (-2 + 7x)
(12(-2 + 7x) + 2x * (-2 + 7x)) = 0
((-2 * 12 + 7x * 12) + 2x * (-2 + 7x)) = 0
((-24 + 84x) + 2x * (-2 + 7x)) = 0
(-24 + 84x + (-2 * 2x + 7x * 2x)) = 0
(-24 + 84x + (-4x + 14x2)) = 0

Combine like terms: 84x + -4x = 80x
(-24 + 80x + 14x2) = 0

Solving
-24 + 80x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 40x + 7x2) = 0

Factor a trinomial.
2((-6 + -1x)(2 + -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 '(2 + -7x)' equal to zero and attempt to solve:

Simplifying
2 + -7x = 0

Solving
2 + -7x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857
Solution
x = {-6, 0.2857142857}

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