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

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

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