(3x-18)(2x+7)=0

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Solution for (3x-18)(2x+7)=0 equation: 


Simplifying
(3x + -18)(2x + 7) = 0

Reorder the terms:
(-18 + 3x)(2x + 7) = 0

Reorder the terms:
(-18 + 3x)(7 + 2x) = 0

Multiply (-18 + 3x) * (7 + 2x)
(-18(7 + 2x) + 3x * (7 + 2x)) = 0
((7 * -18 + 2x * -18) + 3x * (7 + 2x)) = 0
((-126 + -36x) + 3x * (7 + 2x)) = 0
(-126 + -36x + (7 * 3x + 2x * 3x)) = 0
(-126 + -36x + (21x + 6x2)) = 0

Combine like terms: -36x + 21x = -15x
(-126 + -15x + 6x2) = 0

Solving
-126 + -15x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-42 + -5x + 2x2) = 0

Factor a trinomial.
3((-7 + -2x)(6 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-3.5, 6}

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