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

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

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

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

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

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

Combine like terms: 18x + -6x = 12x
(-54 + 12x + 2x2) = 0

Solving
-54 + 12x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + 6x + x2) = 0

Factor a trinomial.
2((-9 + -1x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
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 = {-9, 3}