(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}