6x+5=18x(2x-1)

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Solution for 6x+5=18x(2x-1) equation:


Simplifying
6x + 5 = 18x(2x + -1)

Reorder the terms:
5 + 6x = 18x(2x + -1)

Reorder the terms:
5 + 6x = 18x(-1 + 2x)
5 + 6x = (-1 * 18x + 2x * 18x)
5 + 6x = (-18x + 36x2)

Solving
5 + 6x = -18x + 36x2

Solving for variable 'x'.

Combine like terms: 6x + 18x = 24x
5 + 24x + -36x2 = -18x + 36x2 + 18x + -36x2

Reorder the terms:
5 + 24x + -36x2 = -18x + 18x + 36x2 + -36x2

Combine like terms: -18x + 18x = 0
5 + 24x + -36x2 = 0 + 36x2 + -36x2
5 + 24x + -36x2 = 36x2 + -36x2

Combine like terms: 36x2 + -36x2 = 0
5 + 24x + -36x2 = 0

Factor a trinomial.
(5 + -6x)(1 + 6x) = 0


Subproblem 1
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 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 + -6x = 0 + -5

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

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

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333

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

Simplifying
1 + 6x = 0

Solving
1 + 6x = 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 + 6x = 0 + -1

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

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

Divide each side by '6'.
x = -0.1666666667

Simplifying
x = -0.1666666667
Solution
x = {0.8333333333, -0.1666666667}

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