(4w+7)(4-w)=0

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Solution for (4w+7)(4-w)=0 equation: 


Simplifying
(4w + 7)(4 + -1w) = 0

Reorder the terms:
(7 + 4w)(4 + -1w) = 0

Multiply (7 + 4w) * (4 + -1w)
(7(4 + -1w) + 4w * (4 + -1w)) = 0
((4 * 7 + -1w * 7) + 4w * (4 + -1w)) = 0
((28 + -7w) + 4w * (4 + -1w)) = 0
(28 + -7w + (4 * 4w + -1w * 4w)) = 0
(28 + -7w + (16w + -4w2)) = 0

Combine like terms: -7w + 16w = 9w
(28 + 9w + -4w2) = 0

Solving
28 + 9w + -4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(4 + -1w)(7 + 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 '(7 + 4w)' equal to zero and attempt to solve:

Simplifying
7 + 4w = 0

Solving
7 + 4w = 0

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

Add '-7' to each side of the equation.
7 + -7 + 4w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4w = 0 + -7
4w = 0 + -7

Combine like terms: 0 + -7 = -7
4w = -7

Divide each side by '4'.
w = -1.75

Simplifying
w = -1.75
Solution
w = {4, -1.75}

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