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

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


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

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

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

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

Combine like terms: -54x + 63x = 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((-3 + -2x)(9 + -7x)) = 0

Ignore the factor 3.

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 '(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
Solution
x = {-1.5, 1.285714286}

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