(4+w)(3w-8)=0

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Solution for (4+w)(3w-8)=0 equation: 


Simplifying
(4 + w)(3w + -8) = 0

Reorder the terms:
(4 + w)(-8 + 3w) = 0

Multiply (4 + w) * (-8 + 3w)
(4(-8 + 3w) + w(-8 + 3w)) = 0
((-8 * 4 + 3w * 4) + w(-8 + 3w)) = 0
((-32 + 12w) + w(-8 + 3w)) = 0
(-32 + 12w + (-8 * w + 3w * w)) = 0
(-32 + 12w + (-8w + 3w2)) = 0

Combine like terms: 12w + -8w = 4w
(-32 + 4w + 3w2) = 0

Solving
-32 + 4w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-4 + -1w)(8 + -3w) = 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 '(8 + -3w)' equal to zero and attempt to solve:

Simplifying
8 + -3w = 0

Solving
8 + -3w = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3w = 0 + -8
-3w = 0 + -8

Combine like terms: 0 + -8 = -8
-3w = -8

Divide each side by '-3'.
w = 2.666666667

Simplifying
w = 2.666666667
Solution
w = {-4, 2.666666667}

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