(3x-7)(9x+6)=0

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Solution for (3x-7)(9x+6)=0 equation: 


Simplifying
(3x + -7)(9x + 6) = 0

Reorder the terms:
(-7 + 3x)(9x + 6) = 0

Reorder the terms:
(-7 + 3x)(6 + 9x) = 0

Multiply (-7 + 3x) * (6 + 9x)
(-7(6 + 9x) + 3x * (6 + 9x)) = 0
((6 * -7 + 9x * -7) + 3x * (6 + 9x)) = 0
((-42 + -63x) + 3x * (6 + 9x)) = 0
(-42 + -63x + (6 * 3x + 9x * 3x)) = 0
(-42 + -63x + (18x + 27x2)) = 0

Combine like terms: -63x + 18x = -45x
(-42 + -45x + 27x2) = 0

Solving
-42 + -45x + 27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + -15x + 9x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 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 + -3x = 0 + 2

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

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

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 2
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
Solution
x = {-0.6666666667, 2.333333333}

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