54=w(2w+3)

Solution for 54=w(2w+3) equation:

Simplifying
54 = w(2w + 3)

Reorder the terms:
54 = w(3 + 2w)
54 = (3 * w + 2w * w)
54 = (3w + 2w2)

Solving
54 = 3w + 2w2

Solving for variable 'w'.

Reorder the terms:
54 + -3w + -2w2 = 3w + -3w + 2w2 + -2w2

Combine like terms: 3w + -3w = 0
54 + -3w + -2w2 = 0 + 2w2 + -2w2
54 + -3w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
54 + -3w + -2w2 = 0

Factor a trinomial.
(9 + -2w)(6 + w) = 0

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

Simplifying
9 + -2w = 0

Solving
9 + -2w = 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 + -2w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2w = 0 + -9
-2w = 0 + -9

Combine like terms: 0 + -9 = -9
-2w = -9

Divide each side by '-2'.
w = 4.5

Simplifying
w = 4.5
Subproblem 2
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 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 + w = 0 + -6

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

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

Simplifying
w = -6
Solution
w = {4.5, -6}