x^2+3x=15+x

Solution for x^2+3x=15+x equation:

Simplifying
x2 + 3x = 15 + x

Reorder the terms:
3x + x2 = 15 + x

Solving
3x + x2 = 15 + x

Solving for variable 'x'.

Reorder the terms:
-15 + 3x + -1x + x2 = 15 + x + -15 + -1x

Combine like terms: 3x + -1x = 2x
-15 + 2x + x2 = 15 + x + -15 + -1x

Reorder the terms:
-15 + 2x + x2 = 15 + -15 + x + -1x

Combine like terms: 15 + -15 = 0
-15 + 2x + x2 = 0 + x + -1x
-15 + 2x + x2 = x + -1x

Combine like terms: x + -1x = 0
-15 + 2x + x2 = 0

Factor a trinomial.
(-5 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
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 = {-5, 3}