4x+x^2+x^2=16

Solution for 4x+x^2+x^2=16 equation:

Simplifying
4x + x2 + x2 = 16

Combine like terms: x2 + x2 = 2x2
4x + 2x2 = 16

Solving
4x + 2x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + 4x + 2x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 2x + x2) = 0

Factor a trinomial.
2((-4 + -1x)(2 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

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

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

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
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
Solution
x = {-4, 2}