x(x+18)=6x(x-1)-5

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Solution for x(x+18)=6x(x-1)-5 equation: 


Simplifying
x(x + 18) = 6x(x + -1) + -5

Reorder the terms:
x(18 + x) = 6x(x + -1) + -5
(18 * x + x * x) = 6x(x + -1) + -5
(18x + x2) = 6x(x + -1) + -5

Reorder the terms:
18x + x2 = 6x(-1 + x) + -5
18x + x2 = (-1 * 6x + x * 6x) + -5
18x + x2 = (-6x + 6x2) + -5

Reorder the terms:
18x + x2 = -5 + -6x + 6x2

Solving
18x + x2 = -5 + -6x + 6x2

Solving for variable 'x'.

Reorder the terms:
5 + 18x + 6x + x2 + -6x2 = -5 + -6x + 6x2 + 5 + 6x + -6x2

Combine like terms: 18x + 6x = 24x
5 + 24x + x2 + -6x2 = -5 + -6x + 6x2 + 5 + 6x + -6x2

Combine like terms: x2 + -6x2 = -5x2
5 + 24x + -5x2 = -5 + -6x + 6x2 + 5 + 6x + -6x2

Reorder the terms:
5 + 24x + -5x2 = -5 + 5 + -6x + 6x + 6x2 + -6x2

Combine like terms: -5 + 5 = 0
5 + 24x + -5x2 = 0 + -6x + 6x + 6x2 + -6x2
5 + 24x + -5x2 = -6x + 6x + 6x2 + -6x2

Combine like terms: -6x + 6x = 0
5 + 24x + -5x2 = 0 + 6x2 + -6x2
5 + 24x + -5x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
5 + 24x + -5x2 = 0

Factor a trinomial.
(5 + -1x)(1 + 5x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(1 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

Solving
1 + 5x = 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 + 5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5x = 0 + -1
5x = 0 + -1

Combine like terms: 0 + -1 = -1
5x = -1

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {5, -0.2}

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