3w(4w+3)=-8w-6

Solution for 3w(4w+3)=-8w-6 equation:

Simplifying
3w(4w + 3) = -8w + -6

Reorder the terms:
3w(3 + 4w) = -8w + -6
(3 * 3w + 4w * 3w) = -8w + -6
(9w + 12w2) = -8w + -6

Reorder the terms:
9w + 12w2 = -6 + -8w

Solving
9w + 12w2 = -6 + -8w

Solving for variable 'w'.

Reorder the terms:
6 + 9w + 8w + 12w2 = -6 + -8w + 6 + 8w

Combine like terms: 9w + 8w = 17w
6 + 17w + 12w2 = -6 + -8w + 6 + 8w

Reorder the terms:
6 + 17w + 12w2 = -6 + 6 + -8w + 8w

Combine like terms: -6 + 6 = 0
6 + 17w + 12w2 = 0 + -8w + 8w
6 + 17w + 12w2 = -8w + 8w

Combine like terms: -8w + 8w = 0
6 + 17w + 12w2 = 0

Factor a trinomial.
(3 + 4w)(2 + 3w) = 0

Subproblem 1
Set the factor '(3 + 4w)' equal to zero and attempt to solve:

Simplifying
3 + 4w = 0

Solving
3 + 4w = 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 + 4w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4w = 0 + -3
4w = 0 + -3

Combine like terms: 0 + -3 = -3
4w = -3

Divide each side by '4'.
w = -0.75

Simplifying
w = -0.75
Subproblem 2
Set the factor '(2 + 3w)' equal to zero and attempt to solve:

Simplifying
2 + 3w = 0

Solving
2 + 3w = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3w = 0 + -2

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

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

Divide each side by '3'.
w = -0.6666666667

Simplifying
w = -0.6666666667
Solution
w = {-0.75, -0.6666666667}