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

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


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

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

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

Multiply (-9 + 7x) * (6 + 3x)
(-9(6 + 3x) + 7x * (6 + 3x)) = 0
((6 * -9 + 3x * -9) + 7x * (6 + 3x)) = 0
((-54 + -27x) + 7x * (6 + 3x)) = 0
(-54 + -27x + (6 * 7x + 3x * 7x)) = 0
(-54 + -27x + (42x + 21x2)) = 0

Combine like terms: -27x + 42x = 15x
(-54 + 15x + 21x2) = 0

Solving
-54 + 15x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + 5x + 7x2) = 0

Factor a trinomial.
3((-2 + -1x)(9 + -7x)) = 0

Ignore the factor 3.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 1.285714286}

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