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

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


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

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

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

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

Combine like terms: 18x + -63x = -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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