(2x-18)(3x+9)=0

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Solution for (2x-18)(3x+9)=0 equation: 


Simplifying
(2x + -18)(3x + 9) = 0

Reorder the terms:
(-18 + 2x)(3x + 9) = 0

Reorder the terms:
(-18 + 2x)(9 + 3x) = 0

Multiply (-18 + 2x) * (9 + 3x)
(-18(9 + 3x) + 2x * (9 + 3x)) = 0
((9 * -18 + 3x * -18) + 2x * (9 + 3x)) = 0
((-162 + -54x) + 2x * (9 + 3x)) = 0
(-162 + -54x + (9 * 2x + 3x * 2x)) = 0
(-162 + -54x + (18x + 6x2)) = 0

Combine like terms: -54x + 18x = -36x
(-162 + -36x + 6x2) = 0

Solving
-162 + -36x + 6x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
6((-3 + -1x)(9 + -1x)) = 0

Ignore the factor 6.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-3, 9}

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