3x(x+6)-x=2x+18

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Solution for 3x(x+6)-x=2x+18 equation: 


Simplifying
3x(x + 6) + -1x = 2x + 18

Reorder the terms:
3x(6 + x) + -1x = 2x + 18
(6 * 3x + x * 3x) + -1x = 2x + 18
(18x + 3x2) + -1x = 2x + 18

Reorder the terms:
18x + -1x + 3x2 = 2x + 18

Combine like terms: 18x + -1x = 17x
17x + 3x2 = 2x + 18

Reorder the terms:
17x + 3x2 = 18 + 2x

Solving
17x + 3x2 = 18 + 2x

Solving for variable 'x'.

Reorder the terms:
-18 + 17x + -2x + 3x2 = 18 + 2x + -18 + -2x

Combine like terms: 17x + -2x = 15x
-18 + 15x + 3x2 = 18 + 2x + -18 + -2x

Reorder the terms:
-18 + 15x + 3x2 = 18 + -18 + 2x + -2x

Combine like terms: 18 + -18 = 0
-18 + 15x + 3x2 = 0 + 2x + -2x
-18 + 15x + 3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-18 + 15x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 5x + x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-6, 1}

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