3w^2+w=30

Solution for 3w^2+w=30 equation:

Simplifying
3w2 + w = 30

Reorder the terms:
w + 3w2 = 30

Solving
w + 3w2 = 30

Solving for variable 'w'.

Reorder the terms:
-30 + w + 3w2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + w + 3w2 = 0

Factor a trinomial.
(-10 + -3w)(3 + -1w) = 0

Subproblem 1
Set the factor '(-10 + -3w)' equal to zero and attempt to solve:

Simplifying
-10 + -3w = 0

Solving
-10 + -3w = 0

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

Add '10' to each side of the equation.
-10 + 10 + -3w = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3w = 0 + 10
-3w = 0 + 10

Combine like terms: 0 + 10 = 10
-3w = 10

Divide each side by '-3'.
w = -3.333333333

Simplifying
w = -3.333333333
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 = {-3.333333333, 3}