x+x+x^2+x^2=84

Solution for x+x+x^2+x^2=84 equation:

Simplifying
x + x + x2 + x2 = 84

Combine like terms: x + x = 2x
2x + x2 + x2 = 84

Combine like terms: x2 + x2 = 2x2
2x + 2x2 = 84

Solving
2x + 2x2 = 84

Solving for variable 'x'.

Reorder the terms:
-84 + 2x + 2x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-42 + x + x2) = 0

Factor a trinomial.
2((-7 + -1x)(6 + -1x)) = 0

Ignore the factor 2.
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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-7, 6}