w=2w^2-6

Solution for w=2w^2-6 equation:

Simplifying
w = 2w2 + -6

Reorder the terms:
w = -6 + 2w2

Solving
w = -6 + 2w2

Solving for variable 'w'.

Reorder the terms:
6 + w + -2w2 = -6 + 2w2 + 6 + -2w2

Reorder the terms:
6 + w + -2w2 = -6 + 6 + 2w2 + -2w2

Combine like terms: -6 + 6 = 0
6 + w + -2w2 = 0 + 2w2 + -2w2
6 + w + -2w2 = 2w2 + -2w2

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

Factor a trinomial.
(2 + -1w)(3 + 2w) = 0

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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 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 + -1w = 0 + -2

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

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

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Subproblem 2
Set the factor '(3 + 2w)' equal to zero and attempt to solve:

Simplifying
3 + 2w = 0

Solving
3 + 2w = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2w = 0 + -3
2w = 0 + -3

Combine like terms: 0 + -3 = -3
2w = -3

Divide each side by '2'.
w = -1.5

Simplifying
w = -1.5
Solution
w = {2, -1.5}