40x=-2x^2

Solution for 40x=-2x^2 equation:

Simplifying
40x = -2x2

Solving
40x = -2x2

Solving for variable 'x'.

Combine like terms: -2x2 + 2x2 = 0
40x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(20 + x) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(20 + x)' equal to zero and attempt to solve:

Simplifying
20 + x = 0

Solving
20 + x = 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 + x = 0 + -20

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

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

Simplifying
x = -20
Solution
x = {0, -20}