27=w(2w-3)

Solution for 27=w(2w-3) equation:

Simplifying
27 = w(2w + -3)

Reorder the terms:
27 = w(-3 + 2w)
27 = (-3 * w + 2w * w)
27 = (-3w + 2w2)

Solving
27 = -3w + 2w2

Solving for variable 'w'.

Reorder the terms:
27 + 3w + -2w2 = -3w + 3w + 2w2 + -2w2

Combine like terms: -3w + 3w = 0
27 + 3w + -2w2 = 0 + 2w2 + -2w2
27 + 3w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
27 + 3w + -2w2 = 0

Factor a trinomial.
(9 + -2w)(3 + 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 '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

Solving
3 + w = 0

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

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

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

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

Simplifying
w = -3
Solution
w = {4.5, -3}