x(3x+2)=(x^2+4)

Solution for x(3x+2)=(x^2+4) equation:

Simplifying
x(3x + 2) = (x2 + 4)

Reorder the terms:
x(2 + 3x) = (x2 + 4)
(2 * x + 3x * x) = (x2 + 4)
(2x + 3x2) = (x2 + 4)

Reorder the terms:
2x + 3x2 = (4 + x2)

Remove parenthesis around (4 + x2)
2x + 3x2 = 4 + x2

Solving
2x + 3x2 = 4 + x2

Solving for variable 'x'.

Reorder the terms:
-4 + 2x + 3x2 + -1x2 = 4 + x2 + -4 + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-4 + 2x + 2x2 = 4 + x2 + -4 + -1x2

Reorder the terms:
-4 + 2x + 2x2 = 4 + -4 + x2 + -1x2

Combine like terms: 4 + -4 = 0
-4 + 2x + 2x2 = 0 + x2 + -1x2
-4 + 2x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + 2x + 2x2 = 0

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

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

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
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
Solution
x = {-2, 1}