3x(x+18)=x+18

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Solution for 3x(x+18)=x+18 equation: 


Simplifying
3x(x + 18) = x + 18

Reorder the terms:
3x(18 + x) = x + 18
(18 * 3x + x * 3x) = x + 18
(54x + 3x2) = x + 18

Reorder the terms:
54x + 3x2 = 18 + x

Solving
54x + 3x2 = 18 + x

Solving for variable 'x'.

Reorder the terms:
-18 + 54x + -1x + 3x2 = 18 + x + -18 + -1x

Combine like terms: 54x + -1x = 53x
-18 + 53x + 3x2 = 18 + x + -18 + -1x

Reorder the terms:
-18 + 53x + 3x2 = 18 + -18 + x + -1x

Combine like terms: 18 + -18 = 0
-18 + 53x + 3x2 = 0 + x + -1x
-18 + 53x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
-18 + 53x + 3x2 = 0

Factor a trinomial.
(-18 + -1x)(1 + -3x) = 0


Subproblem 1
Set the factor '(-18 + -1x)' equal to zero and attempt to solve:

Simplifying
-18 + -1x = 0

Solving
-18 + -1x = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1x = 0 + 18
-1x = 0 + 18

Combine like terms: 0 + 18 = 18
-1x = 18

Divide each side by '-1'.
x = -18

Simplifying
x = -18

Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-18, 0.3333333333}

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