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

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

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

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

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

Combine like terms: -2x + x = -1x
-3 + 5x = 6 + -1x + x2

Solving
-3 + 5x = 6 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
-3 + -6 + 5x + x + -1x2 = 6 + -1x + x2 + -6 + x + -1x2

Combine like terms: -3 + -6 = -9
-9 + 5x + x + -1x2 = 6 + -1x + x2 + -6 + x + -1x2

Combine like terms: 5x + x = 6x
-9 + 6x + -1x2 = 6 + -1x + x2 + -6 + x + -1x2

Reorder the terms:
-9 + 6x + -1x2 = 6 + -6 + -1x + x + x2 + -1x2

Combine like terms: 6 + -6 = 0
-9 + 6x + -1x2 = 0 + -1x + x + x2 + -1x2
-9 + 6x + -1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
-9 + 6x + -1x2 = 0 + x2 + -1x2
-9 + 6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-9 + 6x + -1x2 = 0

Factor a trinomial.
(-3 + x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {3, 3}