(4w-7)(5-w)=0

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Solution for (4w-7)(5-w)=0 equation: 


Simplifying
(4w + -7)(5 + -1w) = 0

Reorder the terms:
(-7 + 4w)(5 + -1w) = 0

Multiply (-7 + 4w) * (5 + -1w)
(-7(5 + -1w) + 4w * (5 + -1w)) = 0
((5 * -7 + -1w * -7) + 4w * (5 + -1w)) = 0
((-35 + 7w) + 4w * (5 + -1w)) = 0
(-35 + 7w + (5 * 4w + -1w * 4w)) = 0
(-35 + 7w + (20w + -4w2)) = 0

Combine like terms: 7w + 20w = 27w
(-35 + 27w + -4w2) = 0

Solving
-35 + 27w + -4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-5 + w)(7 + -4w) = 0


Subproblem 1
Set the factor '(-5 + w)' equal to zero and attempt to solve:

Simplifying
-5 + w = 0

Solving
-5 + w = 0

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

Add '5' to each side of the equation.
-5 + 5 + w = 0 + 5

Combine like terms: -5 + 5 = 0
0 + w = 0 + 5
w = 0 + 5

Combine like terms: 0 + 5 = 5
w = 5

Simplifying
w = 5

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 = {5, 1.75}

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