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

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


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

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

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

Multiply (9 + 6x) * (-6 + 9x)
(9(-6 + 9x) + 6x * (-6 + 9x)) = 0
((-6 * 9 + 9x * 9) + 6x * (-6 + 9x)) = 0
((-54 + 81x) + 6x * (-6 + 9x)) = 0
(-54 + 81x + (-6 * 6x + 9x * 6x)) = 0
(-54 + 81x + (-36x + 54x2)) = 0

Combine like terms: 81x + -36x = 45x
(-54 + 45x + 54x2) = 0

Solving
-54 + 45x + 54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-6 + 5x + 6x2) = 0

Factor a trinomial.
9((-3 + -2x)(2 + -3x)) = 0

Ignore the factor 9.

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

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

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

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

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
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
Solution
x = {-1.5, 0.6666666667}

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