x(3x+1)=x^2+15

Solution for x(3x+1)=x^2+15 equation:

Simplifying
x(3x + 1) = x2 + 15

Reorder the terms:
x(1 + 3x) = x2 + 15
(1 * x + 3x * x) = x2 + 15
(1x + 3x2) = x2 + 15

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

Solving
1x + 3x2 = 15 + x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(-3 + -1x)(5 + -2x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-3, 2.5}