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

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


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

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

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

Combine like terms: 16w + 7w = 23w
(-28 + 23w + -4w2) = 0

Solving
-28 + 23w + -4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-4 + w)(7 + -4w) = 0


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

Simplifying
-4 + w = 0

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

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

Combine like terms: 0 + 4 = 4
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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