2w^2+w=10

Solution for 2w^2+w=10 equation:

Simplifying
2w2 + w = 10

Reorder the terms:
w + 2w2 = 10

Solving
w + 2w2 = 10

Solving for variable 'w'.

Reorder the terms:
-10 + w + 2w2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + w + 2w2 = 0

Factor a trinomial.
(-5 + -2w)(2 + -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 '(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 = {-2.5, 2}