(3w-1)(w)=30

Solution for (3w-1)(w)=30 equation:

Simplifying
(3w + -1)(w) = 30

Reorder the terms:
(-1 + 3w)(w) = 30

Reorder the terms for easier multiplication:
w(-1 + 3w) = 30
(-1 * w + 3w * w) = 30
(-1w + 3w2) = 30

Solving
-1w + 3w2 = 30

Solving for variable 'w'.

Reorder the terms:
-30 + -1w + 3w2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -1w + 3w2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
w = {-3, 3.333333333}