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

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


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

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

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

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

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

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

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

Solving
x = 5x + x2

Solving for variable 'x'.

Combine like terms: x + -5x = -4x
-4x + -1x2 = 5x + x2 + -5x + -1x2

Reorder the terms:
-4x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
-4x + -1x2 = 0 + x2 + -1x2
-4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(4 + x) = 0

Ignore the factor -1.

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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {0, -4}

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