3w^2=2w(4w+3)

Solution for 3w^2=2w(4w+3) equation:

Simplifying
3w2 = 2w(4w + 3)

Reorder the terms:
3w2 = 2w(3 + 4w)
3w2 = (3 * 2w + 4w * 2w)
3w2 = (6w + 8w2)

Solving
3w2 = 6w + 8w2

Solving for variable 'w'.

Reorder the terms:
-6w + 3w2 + -8w2 = 6w + 8w2 + -6w + -8w2

Combine like terms: 3w2 + -8w2 = -5w2
-6w + -5w2 = 6w + 8w2 + -6w + -8w2

Reorder the terms:
-6w + -5w2 = 6w + -6w + 8w2 + -8w2

Combine like terms: 6w + -6w = 0
-6w + -5w2 = 0 + 8w2 + -8w2
-6w + -5w2 = 8w2 + -8w2

Combine like terms: 8w2 + -8w2 = 0
-6w + -5w2 = 0

Factor out the Greatest Common Factor (GCF), '-1w'.
-1w(6 + 5w) = 0

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

Simplifying
w = 0

Solving
w = 0

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

Simplifying
w = 0
Subproblem 2
Set the factor '(6 + 5w)' equal to zero and attempt to solve:

Simplifying
6 + 5w = 0

Solving
6 + 5w = 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 + 5w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5w = 0 + -6
5w = 0 + -6

Combine like terms: 0 + -6 = -6
5w = -6

Divide each side by '5'.
w = -1.2

Simplifying
w = -1.2
Solution
w = {0, -1.2}