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

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


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

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

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

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

Add '-5' to each side of the equation.
5 + -1x + -5 + 3x2 = 5 + -5 + 5x

Reorder the terms:
5 + -5 + -1x + 3x2 = 5 + -5 + 5x

Combine like terms: 5 + -5 = 0
0 + -1x + 3x2 = 5 + -5 + 5x
-1x + 3x2 = 5 + -5 + 5x

Combine like terms: 5 + -5 = 0
-1x + 3x2 = 0 + 5x
-1x + 3x2 = 5x

Solving
-1x + 3x2 = 5x

Solving for variable 'x'.

Reorder the terms:
-1x + -5x + 3x2 = 5x + -5x

Combine like terms: -1x + -5x = -6x
-6x + 3x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-2 + x) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

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

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

Simplifying
x = 2
Solution
x = {0, 2}

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