2(w^2+9)=15w

Solution for 2(w^2+9)=15w equation:

Simplifying
2(w2 + 9) = 15w

Reorder the terms:
2(9 + w2) = 15w
(9 * 2 + w2 * 2) = 15w
(18 + 2w2) = 15w

Solving
18 + 2w2 = 15w

Solving for variable 'w'.

Reorder the terms:
18 + -15w + 2w2 = 15w + -15w

Combine like terms: 15w + -15w = 0
18 + -15w + 2w2 = 0

Factor a trinomial.
(3 + -2w)(6 + -1w) = 0

Subproblem 1
Set the factor '(3 + -2w)' equal to zero and attempt to solve:

Simplifying
3 + -2w = 0

Solving
3 + -2w = 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 + -2w = 0 + -3

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

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

Divide each side by '-2'.
w = 1.5

Simplifying
w = 1.5
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 = {1.5, 6}