(2x+30)(3x-18)=0

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Solution for (2x+30)(3x-18)=0 equation:


Simplifying
(2x + 30)(3x + -18) = 0

Reorder the terms:
(30 + 2x)(3x + -18) = 0

Reorder the terms:
(30 + 2x)(-18 + 3x) = 0

Multiply (30 + 2x) * (-18 + 3x)
(30(-18 + 3x) + 2x * (-18 + 3x)) = 0
((-18 * 30 + 3x * 30) + 2x * (-18 + 3x)) = 0
((-540 + 90x) + 2x * (-18 + 3x)) = 0
(-540 + 90x + (-18 * 2x + 3x * 2x)) = 0
(-540 + 90x + (-36x + 6x2)) = 0

Combine like terms: 90x + -36x = 54x
(-540 + 54x + 6x2) = 0

Solving
-540 + 54x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-90 + 9x + x2) = 0

Factor a trinomial.
6((-15 + -1x)(6 + -1x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15

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 = {-15, 6}

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