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

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

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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -3 + -5 = -8
-8 + -5x + -1x + 2x2 = 5 + x + -5 + -1x

Combine like terms: -5x + -1x = -6x
-8 + -6x + 2x2 = 5 + x + -5 + -1x

Reorder the terms:
-8 + -6x + 2x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
-8 + -6x + 2x2 = 0 + x + -1x
-8 + -6x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-8 + -6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -3x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(4 + -1x)) = 0

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

Simplifying
-1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1, 4}