x^2-2+3x+6=5x+4

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Solution for x^2-2+3x+6=5x+4 equation: 


Simplifying
x2 + -2 + 3x + 6 = 5x + 4

Reorder the terms:
-2 + 6 + 3x + x2 = 5x + 4

Combine like terms: -2 + 6 = 4
4 + 3x + x2 = 5x + 4

Reorder the terms:
4 + 3x + x2 = 4 + 5x

Add '-4' to each side of the equation.
4 + 3x + -4 + x2 = 4 + -4 + 5x

Reorder the terms:
4 + -4 + 3x + x2 = 4 + -4 + 5x

Combine like terms: 4 + -4 = 0
0 + 3x + x2 = 4 + -4 + 5x
3x + x2 = 4 + -4 + 5x

Combine like terms: 4 + -4 = 0
3x + x2 = 0 + 5x
3x + x2 = 5x

Solving
3x + x2 = 5x

Solving for variable 'x'.

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

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

Combine like terms: 5x + -5x = 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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