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

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


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

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

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

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

Combine like terms: -42x + 27x = -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((-9 + -7x)(2 + -1x)) = 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 '(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
Solution
x = {-1.285714286, 2}

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