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

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

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

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

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

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