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

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


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

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

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

Add '2' to each side of the equation.
-2 + 5x + 2 + x2 = -2 + 2 + 3x

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

Combine like terms: -2 + 2 = 0
0 + 5x + x2 = -2 + 2 + 3x
5x + x2 = -2 + 2 + 3x

Combine like terms: -2 + 2 = 0
5x + x2 = 0 + 3x
5x + x2 = 3x

Solving
5x + x2 = 3x

Solving for variable 'x'.

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

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

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

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


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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