2x^2+20x=400

Solution for 2x^2+20x=400 equation:

Simplifying
2x2 + 20x = 400

Reorder the terms:
20x + 2x2 = 400

Solving
20x + 2x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + 20x + 2x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + 20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-200 + 10x + x2) = 0

Factor a trinomial.
2((-20 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-20, 10}