(2w+3)(w)=54

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

Simplifying
(2w + 3)(w) = 54

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

Reorder the terms for easier multiplication:
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.
(-6 + -1w)(9 + -2w) = 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 + -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
Solution
w = {-6, 4.5}