2w^2-w=15

Solution for 2w^2-w=15 equation:

Simplifying
2w2 + -1w = 15

Reorder the terms:
-1w + 2w2 = 15

Solving
-1w + 2w2 = 15

Solving for variable 'w'.

Reorder the terms:
-15 + -1w + 2w2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -1w + 2w2 = 0

Factor a trinomial.
(-5 + -2w)(3 + -1w) = 0

Subproblem 1
Set the factor '(-5 + -2w)' equal to zero and attempt to solve:

Simplifying
-5 + -2w = 0

Solving
-5 + -2w = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2w = 0 + 5

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

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

Divide each side by '-2'.
w = -2.5

Simplifying
w = -2.5
Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 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 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {-2.5, 3}