6x(x-1)=2x(x+3)-5

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Solution for 6x(x-1)=2x(x+3)-5 equation: 


Simplifying
6x(x + -1) = 2x(x + 3) + -5

Reorder the terms:
6x(-1 + x) = 2x(x + 3) + -5
(-1 * 6x + x * 6x) = 2x(x + 3) + -5
(-6x + 6x2) = 2x(x + 3) + -5

Reorder the terms:
-6x + 6x2 = 2x(3 + x) + -5
-6x + 6x2 = (3 * 2x + x * 2x) + -5
-6x + 6x2 = (6x + 2x2) + -5

Reorder the terms:
-6x + 6x2 = -5 + 6x + 2x2

Solving
-6x + 6x2 = -5 + 6x + 2x2

Solving for variable 'x'.

Reorder the terms:
5 + -6x + -6x + 6x2 + -2x2 = -5 + 6x + 2x2 + 5 + -6x + -2x2

Combine like terms: -6x + -6x = -12x
5 + -12x + 6x2 + -2x2 = -5 + 6x + 2x2 + 5 + -6x + -2x2

Combine like terms: 6x2 + -2x2 = 4x2
5 + -12x + 4x2 = -5 + 6x + 2x2 + 5 + -6x + -2x2

Reorder the terms:
5 + -12x + 4x2 = -5 + 5 + 6x + -6x + 2x2 + -2x2

Combine like terms: -5 + 5 = 0
5 + -12x + 4x2 = 0 + 6x + -6x + 2x2 + -2x2
5 + -12x + 4x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
5 + -12x + 4x2 = 0 + 2x2 + -2x2
5 + -12x + 4x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5 + -12x + 4x2 = 0

Factor a trinomial.
(1 + -2x)(5 + -2x) = 0


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0.5, 2.5}

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