2w^2+w-21=0

Solution for 2w^2+w-21=0 equation:

Simplifying
2w2 + w + -21 = 0

Reorder the terms:
-21 + w + 2w2 = 0

Solving
-21 + w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-7 + -2w)(3 + -1w) = 0

Subproblem 1
Set the factor '(-7 + -2w)' equal to zero and attempt to solve:

Simplifying
-7 + -2w = 0

Solving
-7 + -2w = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2w = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2w = 0 + 7
-2w = 0 + 7

Combine like terms: 0 + 7 = 7
-2w = 7

Divide each side by '-2'.
w = -3.5

Simplifying
w = -3.5
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 = {-3.5, 3}