w(3w+5)=492

Solution for w(3w+5)=492 equation:

Simplifying
w(3w + 5) = 492

Reorder the terms:
w(5 + 3w) = 492
(5 * w + 3w * w) = 492
(5w + 3w2) = 492

Solving
5w + 3w2 = 492

Solving for variable 'w'.

Reorder the terms:
-492 + 5w + 3w2 = 492 + -492

Combine like terms: 492 + -492 = 0
-492 + 5w + 3w2 = 0

Factor a trinomial.
(-41 + -3w)(12 + -1w) = 0

Subproblem 1
Set the factor '(-41 + -3w)' equal to zero and attempt to solve:

Simplifying
-41 + -3w = 0

Solving
-41 + -3w = 0

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

Add '41' to each side of the equation.
-41 + 41 + -3w = 0 + 41

Combine like terms: -41 + 41 = 0
0 + -3w = 0 + 41
-3w = 0 + 41

Combine like terms: 0 + 41 = 41
-3w = 41

Divide each side by '-3'.
w = -13.66666667

Simplifying
w = -13.66666667
Subproblem 2
Set the factor '(12 + -1w)' equal to zero and attempt to solve:

Simplifying
12 + -1w = 0

Solving
12 + -1w = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1w = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1w = 0 + -12
-1w = 0 + -12

Combine like terms: 0 + -12 = -12
-1w = -12

Divide each side by '-1'.
w = 12

Simplifying
w = 12
Solution
w = {-13.66666667, 12}