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

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


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

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

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

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

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

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

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

Solving
-3x + 2x2 = x

Solving for variable 'x'.

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

Combine like terms: -3x + -1x = -4x
-4x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-4x + 2x2 = 0

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

Ignore the factor 2.

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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