x^2+3x=x-1

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


Simplifying
x2 + 3x = x + -1

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

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

Solving
3x + x2 = -1 + x

Solving for variable 'x'.

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

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

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

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

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

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

Subproblem 1

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

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 = {-1, -1}

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