6w^2=9+15w

Solution for 6w^2=9+15w equation:

Simplifying
6w2 = 9 + 15w

Solving
6w2 = 9 + 15w

Solving for variable 'w'.

Reorder the terms:
-9 + -15w + 6w2 = 9 + 15w + -9 + -15w

Reorder the terms:
-9 + -15w + 6w2 = 9 + -9 + 15w + -15w

Combine like terms: 9 + -9 = 0
-9 + -15w + 6w2 = 0 + 15w + -15w
-9 + -15w + 6w2 = 15w + -15w

Combine like terms: 15w + -15w = 0
-9 + -15w + 6w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -5w + 2w2) = 0

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

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

Simplifying
-1 + -2w = 0

Solving
-1 + -2w = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2w = 0 + 1
-2w = 0 + 1

Combine like terms: 0 + 1 = 1
-2w = 1

Divide each side by '-2'.
w = -0.5

Simplifying
w = -0.5
Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 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 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {-0.5, 3}