5+3x-2x^2=x+1

Solution for 5+3x-2x^2=x+1 equation:

Simplifying
5 + 3x + -2x2 = x + 1

Reorder the terms:
5 + 3x + -2x2 = 1 + x

Solving
5 + 3x + -2x2 = 1 + x

Solving for variable 'x'.

Reorder the terms:
5 + -1 + 3x + -1x + -2x2 = 1 + x + -1 + -1x

Combine like terms: 5 + -1 = 4
4 + 3x + -1x + -2x2 = 1 + x + -1 + -1x

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

Reorder the terms:
4 + 2x + -2x2 = 1 + -1 + x + -1x

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + x + -1x2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {2, -1}