4x+6=x*x-15

Solution for 4x+6=x*x-15 equation:

Simplifying
4x + 6 = x * x + -15

Reorder the terms:
6 + 4x = x * x + -15

Multiply x * x
6 + 4x = x2 + -15

Reorder the terms:
6 + 4x = -15 + x2

Solving
6 + 4x = -15 + x2

Solving for variable 'x'.

Reorder the terms:
6 + 15 + 4x + -1x2 = -15 + x2 + 15 + -1x2

Combine like terms: 6 + 15 = 21
21 + 4x + -1x2 = -15 + x2 + 15 + -1x2

Reorder the terms:
21 + 4x + -1x2 = -15 + 15 + x2 + -1x2

Combine like terms: -15 + 15 = 0
21 + 4x + -1x2 = 0 + x2 + -1x2
21 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
21 + 4x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(3 + x) = 0

Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Subproblem 2
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
Solution
x = {7, -3}