x^2+x^2+10x+20x-150-50=0

Solution for x^2+x^2+10x+20x-150-50=0 equation:

Simplifying
x2 + x2 + 10x + 20x + -150 + -50 = 0

Reorder the terms:
-150 + -50 + 10x + 20x + x2 + x2 = 0

Combine like terms: -150 + -50 = -200
-200 + 10x + 20x + x2 + x2 = 0

Combine like terms: 10x + 20x = 30x
-200 + 30x + x2 + x2 = 0

Combine like terms: x2 + x2 = 2x2
-200 + 30x + 2x2 = 0

Solving
-200 + 30x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-100 + 15x + x2) = 0

Factor a trinomial.
2((-20 + -1x)(5 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve:

Simplifying
-20 + -1x = 0

Solving
-20 + -1x = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1x = 0 + 20
-1x = 0 + 20

Combine like terms: 0 + 20 = 20
-1x = 20

Divide each side by '-1'.
x = -20

Simplifying
x = -20
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-20, 5}