3w^2=17w+6

Solution for 3w^2=17w+6 equation:

Simplifying
3w2 = 17w + 6

Reorder the terms:
3w2 = 6 + 17w

Solving
3w2 = 6 + 17w

Solving for variable 'w'.

Reorder the terms:
-6 + -17w + 3w2 = 6 + 17w + -6 + -17w

Reorder the terms:
-6 + -17w + 3w2 = 6 + -6 + 17w + -17w

Combine like terms: 6 + -6 = 0
-6 + -17w + 3w2 = 0 + 17w + -17w
-6 + -17w + 3w2 = 17w + -17w

Combine like terms: 17w + -17w = 0
-6 + -17w + 3w2 = 0

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

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

Simplifying
-1 + -3w = 0

Solving
-1 + -3w = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3w = 0 + 1

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

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

Divide each side by '-3'.
w = -0.3333333333

Simplifying
w = -0.3333333333
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 = {-0.3333333333, 6}