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

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

Simplifying
(3w + -4)(4w + 6) = 0

Reorder the terms:
(-4 + 3w)(4w + 6) = 0

Reorder the terms:
(-4 + 3w)(6 + 4w) = 0

Multiply (-4 + 3w) * (6 + 4w)
(-4(6 + 4w) + 3w * (6 + 4w)) = 0
((6 * -4 + 4w * -4) + 3w * (6 + 4w)) = 0
((-24 + -16w) + 3w * (6 + 4w)) = 0
(-24 + -16w + (6 * 3w + 4w * 3w)) = 0
(-24 + -16w + (18w + 12w2)) = 0

Combine like terms: -16w + 18w = 2w
(-24 + 2w + 12w2) = 0

Solving
-24 + 2w + 12w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + w + 6w2) = 0

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

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

Simplifying
-3 + -2w = 0

Solving
-3 + -2w = 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 + -2w = 0 + 3

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

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

Divide each side by '-2'.
w = -1.5

Simplifying
w = -1.5
Subproblem 2
Set the factor '(4 + -3w)' equal to zero and attempt to solve:

Simplifying
4 + -3w = 0

Solving
4 + -3w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3w = 0 + -4

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

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

Divide each side by '-3'.
w = 1.333333333

Simplifying
w = 1.333333333
Solution
w = {-1.5, 1.333333333}