(3x-9)(2x+6)=0

Solution for (3x-9)(2x+6)=0 equation:

Simplifying
(3x + -9)(2x + 6) = 0

Reorder the terms:
(-9 + 3x)(2x + 6) = 0

Reorder the terms:
(-9 + 3x)(6 + 2x) = 0

Multiply (-9 + 3x) * (6 + 2x)
(-9(6 + 2x) + 3x * (6 + 2x)) = 0
((6 * -9 + 2x * -9) + 3x * (6 + 2x)) = 0
((-54 + -18x) + 3x * (6 + 2x)) = 0
(-54 + -18x + (6 * 3x + 2x * 3x)) = 0
(-54 + -18x + (18x + 6x2)) = 0

Combine like terms: -18x + 18x = 0
(-54 + 0 + 6x2) = 0
(-54 + 6x2) = 0

Solving
-54 + 6x2 = 0

Solving for variable 'x'.

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

Add '54' to each side of the equation.
-54 + 54 + 6x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + 6x2 = 0 + 54
6x2 = 0 + 54

Combine like terms: 0 + 54 = 54
6x2 = 54

Divide each side by '6'.
x2 = 9

Simplifying
x2 = 9

Take the square root of each side:
x = {-3, 3}