9w^2=6w+3

Solution for 9w^2=6w+3 equation:

Simplifying
9w2 = 6w + 3

Reorder the terms:
9w2 = 3 + 6w

Solving
9w2 = 3 + 6w

Solving for variable 'w'.

Reorder the terms:
-3 + -6w + 9w2 = 3 + 6w + -3 + -6w

Reorder the terms:
-3 + -6w + 9w2 = 3 + -3 + 6w + -6w

Combine like terms: 3 + -3 = 0
-3 + -6w + 9w2 = 0 + 6w + -6w
-3 + -6w + 9w2 = 6w + -6w

Combine like terms: 6w + -6w = 0
-3 + -6w + 9w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -2w + 3w2) = 0

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

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

Simplifying
-1 + -3w = 0

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

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

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

Divide each side by '-3'.
w = -0.3333333333

Simplifying
w = -0.3333333333
Subproblem 2
Set the factor '(1 + -1w)' equal to zero and attempt to solve:

Simplifying
1 + -1w = 0

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

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

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

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

Simplifying
w = 1
Solution
w = {-0.3333333333, 1}