3w^2-w=24

Solution for 3w^2-w=24 equation:

Simplifying
3w2 + -1w = 24

Reorder the terms:
-1w + 3w2 = 24

Solving
-1w + 3w2 = 24

Solving for variable 'w'.

Reorder the terms:
-24 + -1w + 3w2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -1w + 3w2 = 0

Factor a trinomial.
(-8 + -3w)(3 + -1w) = 0

Subproblem 1
Set the factor '(-8 + -3w)' equal to zero and attempt to solve:

Simplifying
-8 + -3w = 0

Solving
-8 + -3w = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3w = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3w = 0 + 8
-3w = 0 + 8

Combine like terms: 0 + 8 = 8
-3w = 8

Divide each side by '-3'.
w = -2.666666667

Simplifying
w = -2.666666667
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 = {-2.666666667, 3}