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

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


Simplifying
2x2 + x + -1 = (3x + 3)(x + -1)

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

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

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

Multiply (3 + 3x) * (-1 + x)
-1 + x + 2x2 = (3(-1 + x) + 3x * (-1 + x))
-1 + x + 2x2 = ((-1 * 3 + x * 3) + 3x * (-1 + x))
-1 + x + 2x2 = ((-3 + 3x) + 3x * (-1 + x))
-1 + x + 2x2 = (-3 + 3x + (-1 * 3x + x * 3x))
-1 + x + 2x2 = (-3 + 3x + (-3x + 3x2))

Combine like terms: 3x + -3x = 0
-1 + x + 2x2 = (-3 + 0 + 3x2)
-1 + x + 2x2 = (-3 + 3x2)

Solving
-1 + x + 2x2 = -3 + 3x2

Solving for variable 'x'.

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

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

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

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

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

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

Factor a trinomial.
(2 + -1x)(1 + x) = 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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {2, -1}

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