10x+2=-8x^2

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

Simplifying
10x + 2 = -8x2

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

Solving
2 + 10x = -8x2

Solving for variable 'x'.

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

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

Factor a trinomial.
2((1 + x)(1 + 4x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {-1, -0.25}