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

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

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

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

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

Multiply (-9 + 3x) * (6 + 7x)
(-9(6 + 7x) + 3x * (6 + 7x)) = 0
((6 * -9 + 7x * -9) + 3x * (6 + 7x)) = 0
((-54 + -63x) + 3x * (6 + 7x)) = 0
(-54 + -63x + (6 * 3x + 7x * 3x)) = 0
(-54 + -63x + (18x + 21x2)) = 0

Combine like terms: -63x + 18x = -45x
(-54 + -45x + 21x2) = 0

Solving
-54 + -45x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + -15x + 7x2) = 0

Factor a trinomial.
3((-6 + -7x)(3 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + -7x)' equal to zero and attempt to solve:

Simplifying
-6 + -7x = 0

Solving
-6 + -7x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -7x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -7x = 0 + 6
-7x = 0 + 6

Combine like terms: 0 + 6 = 6
-7x = 6

Divide each side by '-7'.
x = -0.8571428571

Simplifying
x = -0.8571428571
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.8571428571, 3}