w(3w-1)=102

Solution for w(3w-1)=102 equation:

Simplifying
w(3w + -1) = 102

Reorder the terms:
w(-1 + 3w) = 102
(-1 * w + 3w * w) = 102
(-1w + 3w2) = 102

Solving
-1w + 3w2 = 102

Solving for variable 'w'.

Reorder the terms:
-102 + -1w + 3w2 = 102 + -102

Combine like terms: 102 + -102 = 0
-102 + -1w + 3w2 = 0

Factor a trinomial.
(-17 + -3w)(6 + -1w) = 0

Subproblem 1
Set the factor '(-17 + -3w)' equal to zero and attempt to solve:

Simplifying
-17 + -3w = 0

Solving
-17 + -3w = 0

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

Add '17' to each side of the equation.
-17 + 17 + -3w = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -3w = 0 + 17
-3w = 0 + 17

Combine like terms: 0 + 17 = 17
-3w = 17

Divide each side by '-3'.
w = -5.666666667

Simplifying
w = -5.666666667
Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Solution
w = {-5.666666667, 6}