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

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


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

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

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

Multiply (-9 + 6x) * (9 + 7x)
(-9(9 + 7x) + 6x * (9 + 7x)) = 0
((9 * -9 + 7x * -9) + 6x * (9 + 7x)) = 0
((-81 + -63x) + 6x * (9 + 7x)) = 0
(-81 + -63x + (9 * 6x + 7x * 6x)) = 0
(-81 + -63x + (54x + 42x2)) = 0

Combine like terms: -63x + 54x = -9x
(-81 + -9x + 42x2) = 0

Solving
-81 + -9x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-27 + -3x + 14x2) = 0

Factor a trinomial.
3((-9 + -7x)(3 + -2x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-9 + -7x)' equal to zero and attempt to solve:

Simplifying
-9 + -7x = 0

Solving
-9 + -7x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -7x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -7x = 0 + 9
-7x = 0 + 9

Combine like terms: 0 + 9 = 9
-7x = 9

Divide each side by '-7'.
x = -1.285714286

Simplifying
x = -1.285714286

Subproblem 2
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
Solution
x = {-1.285714286, 1.5}

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