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

Solution for (4+w)(4w-3)=0 equation:

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

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

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

Combine like terms: 16w + -3w = 13w
(-12 + 13w + 4w2) = 0

Solving
-12 + 13w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-4 + -1w)(3 + -4w) = 0

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

Simplifying
-4 + -1w = 0

Solving
-4 + -1w = 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 + -1w = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1w = 0 + 4
-1w = 0 + 4

Combine like terms: 0 + 4 = 4
-1w = 4

Divide each side by '-1'.
w = -4

Simplifying
w = -4
Subproblem 2
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
Solution
w = {-4, 0.75}