8x-2x^2=-10

Solution for 8x-2x^2=-10 equation:

Simplifying
8x + -2x2 = -10

Solving
8x + -2x2 = -10

Solving for variable 'x'.

Reorder the terms:
10 + 8x + -2x2 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + 8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 4x + -1x2) = 0

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

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {5, -1}