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

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Solution for (1-w)(5w-7)=0 equation: 


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

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

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

Combine like terms: 5w + 7w = 12w
(-7 + 12w + -5w2) = 0

Solving
-7 + 12w + -5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-7 + 5w)(1 + -1w) = 0


Subproblem 1
Set the factor '(-7 + 5w)' equal to zero and attempt to solve:

Simplifying
-7 + 5w = 0

Solving
-7 + 5w = 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 + 5w = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 5w = 0 + 7
5w = 0 + 7

Combine like terms: 0 + 7 = 7
5w = 7

Divide each side by '5'.
w = 1.4

Simplifying
w = 1.4

Subproblem 2
Set the factor '(1 + -1w)' equal to zero and attempt to solve:

Simplifying
1 + -1w = 0

Solving
1 + -1w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1w = 0 + -1

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

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

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

Simplifying
w = 1
Solution
w = {1.4, 1}

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