x*(x+1)-2x+1=3x-3

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


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

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

Reorder the terms:
1 + 1x + -2x + x2 = 3x + -3

Combine like terms: 1x + -2x = -1x
1 + -1x + x2 = 3x + -3

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

Solving
1 + -1x + x2 = -3 + 3x

Solving for variable 'x'.

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

Combine like terms: 1 + 3 = 4
4 + -1x + -3x + x2 = -3 + 3x + 3 + -3x

Combine like terms: -1x + -3x = -4x
4 + -4x + x2 = -3 + 3x + 3 + -3x

Reorder the terms:
4 + -4x + x2 = -3 + 3 + 3x + -3x

Combine like terms: -3 + 3 = 0
4 + -4x + x2 = 0 + 3x + -3x
4 + -4x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
4 + -4x + x2 = 0

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


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

Simplifying
2 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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

Simplifying
2 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 2

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

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