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

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

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

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

Solving
6w + 8w2 = 3w2

Solving for variable 'w'.

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

Combine like terms: 3w2 + -3w2 = 0
6w + 5w2 = 0

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

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}