2w^2=w+6

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

Simplifying
2w2 = w + 6

Reorder the terms:
2w2 = 6 + w

Solving
2w2 = 6 + w

Solving for variable 'w'.

Reorder the terms:
-6 + -1w + 2w2 = 6 + w + -6 + -1w

Reorder the terms:
-6 + -1w + 2w2 = 6 + -6 + w + -1w

Combine like terms: 6 + -6 = 0
-6 + -1w + 2w2 = 0 + w + -1w
-6 + -1w + 2w2 = w + -1w

Combine like terms: w + -1w = 0
-6 + -1w + 2w2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
w = {-1.5, 2}