54=w(3+w)

Solution for 54=w(3+w) equation:

Simplifying
54 = w(3 + w)
54 = (3 * w + w * w)
54 = (3w + w2)

Solving
54 = 3w + w2

Solving for variable 'w'.

Reorder the terms:
54 + -3w + -1w2 = 3w + -3w + w2 + -1w2

Combine like terms: 3w + -3w = 0
54 + -3w + -1w2 = 0 + w2 + -1w2
54 + -3w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
54 + -3w + -1w2 = 0

Factor a trinomial.
(6 + -1w)(9 + w) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + w)' equal to zero and attempt to solve:

Simplifying
9 + w = 0

Solving
9 + w = 0

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

Add '-9' to each side of the equation.
9 + -9 + w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + w = 0 + -9
w = 0 + -9

Combine like terms: 0 + -9 = -9
w = -9

Simplifying
w = -9
Solution
w = {6, -9}