w(2w-3)=54

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

Simplifying
w(2w + -3) = 54

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

Solving
-3w + 2w2 = 54

Solving for variable 'w'.

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

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

Factor a trinomial.
(-9 + -2w)(6 + -1w) = 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 + -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 = {-4.5, 6}