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

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


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

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

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

Multiply (-6 + 7x) * (7 + 3x)
3(-6(7 + 3x) + 7x * (7 + 3x)) = 0
3((7 * -6 + 3x * -6) + 7x * (7 + 3x)) = 0
3((-42 + -18x) + 7x * (7 + 3x)) = 0
3(-42 + -18x + (7 * 7x + 3x * 7x)) = 0
3(-42 + -18x + (49x + 21x2)) = 0

Combine like terms: -18x + 49x = 31x
3(-42 + 31x + 21x2) = 0
(-42 * 3 + 31x * 3 + 21x2 * 3) = 0
(-126 + 93x + 63x2) = 0

Solving
-126 + 93x + 63x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-42 + 31x + 21x2) = 0

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

Ignore the factor 3.

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 '(6 + -7x)' equal to zero and attempt to solve:

Simplifying
6 + -7x = 0

Solving
6 + -7x = 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 + -7x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7x = 0 + -6
-7x = 0 + -6

Combine like terms: 0 + -6 = -6
-7x = -6

Divide each side by '-7'.
x = 0.8571428571

Simplifying
x = 0.8571428571
Solution
x = {-2.333333333, 0.8571428571}

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