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

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


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

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

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

Multiply (-7 + 2x) * (7 + 3x)
6(-7(7 + 3x) + 2x * (7 + 3x)) = 0
6((7 * -7 + 3x * -7) + 2x * (7 + 3x)) = 0
6((-49 + -21x) + 2x * (7 + 3x)) = 0
6(-49 + -21x + (7 * 2x + 3x * 2x)) = 0
6(-49 + -21x + (14x + 6x2)) = 0

Combine like terms: -21x + 14x = -7x
6(-49 + -7x + 6x2) = 0
(-49 * 6 + -7x * 6 + 6x2 * 6) = 0
(-294 + -42x + 36x2) = 0

Solving
-294 + -42x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-49 + -7x + 6x2) = 0

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

Ignore the factor 6.

Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve:

Simplifying
-7 + -3x = 0

Solving
-7 + -3x = 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 + -3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3x = 0 + 7
-3x = 0 + 7

Combine like terms: 0 + 7 = 7
-3x = 7

Divide each side by '-3'.
x = -2.333333333

Simplifying
x = -2.333333333

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

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

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

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-2.333333333, 3.5}

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