x^2+2x-5=3x-3

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Solution for x^2+2x-5=3x-3 equation:


Simplifying
x2 + 2x + -5 = 3x + -3

Reorder the terms:
-5 + 2x + x2 = 3x + -3

Reorder the terms:
-5 + 2x + x2 = -3 + 3x

Solving
-5 + 2x + x2 = -3 + 3x

Solving for variable 'x'.

Reorder the terms:
-5 + 3 + 2x + -3x + x2 = -3 + 3x + 3 + -3x

Combine like terms: -5 + 3 = -2
-2 + 2x + -3x + x2 = -3 + 3x + 3 + -3x

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

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

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

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

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

Subproblem 1

Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1

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 = {-1, 2}

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