-5w-2=2w^2

Solution for -5w-2=2w^2 equation:

Simplifying
-5w + -2 = 2w2

Reorder the terms:
-2 + -5w = 2w2

Solving
-2 + -5w = 2w2

Solving for variable 'w'.

Combine like terms: 2w2 + -2w2 = 0
-2 + -5w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 5w + 2w2) = 0

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

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

Simplifying
2 + w = 0

Solving
2 + w = 0

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

Add '-2' to each side of the equation.
2 + -2 + w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + w = 0 + -2
w = 0 + -2

Combine like terms: 0 + -2 = -2
w = -2

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

Simplifying
1 + 2w = 0

Solving
1 + 2w = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2w = 0 + -1
2w = 0 + -1

Combine like terms: 0 + -1 = -1
2w = -1

Divide each side by '2'.
w = -0.5

Simplifying
w = -0.5
Solution
w = {-2, -0.5}