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

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


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

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

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

Multiply (-3 + 2x) * (7 + 6x)
2(-3(7 + 6x) + 2x * (7 + 6x)) = 0
2((7 * -3 + 6x * -3) + 2x * (7 + 6x)) = 0
2((-21 + -18x) + 2x * (7 + 6x)) = 0
2(-21 + -18x + (7 * 2x + 6x * 2x)) = 0
2(-21 + -18x + (14x + 12x2)) = 0

Combine like terms: -18x + 14x = -4x
2(-21 + -4x + 12x2) = 0
(-21 * 2 + -4x * 2 + 12x2 * 2) = 0
(-42 + -8x + 24x2) = 0

Solving
-42 + -8x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -4x + 12x2) = 0

Factor a trinomial.
2((-7 + -6x)(3 + -2x)) = 0

Ignore the factor 2.

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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1.166666667, 1.5}

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