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

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


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

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

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

Multiply (-2 + 7x) * (7 + 6x)
6(-2(7 + 6x) + 7x * (7 + 6x)) = 0
6((7 * -2 + 6x * -2) + 7x * (7 + 6x)) = 0
6((-14 + -12x) + 7x * (7 + 6x)) = 0
6(-14 + -12x + (7 * 7x + 6x * 7x)) = 0
6(-14 + -12x + (49x + 42x2)) = 0

Combine like terms: -12x + 49x = 37x
6(-14 + 37x + 42x2) = 0
(-14 * 6 + 37x * 6 + 42x2 * 6) = 0
(-84 + 222x + 252x2) = 0

Solving
-84 + 222x + 252x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-14 + 37x + 42x2) = 0

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

Ignore the factor 6.

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 '(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 = {-1.166666667, 0.2857142857}

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