(7-w)(2w-1)=0

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Solution for (7-w)(2w-1)=0 equation: 


Simplifying
(7 + -1w)(2w + -1) = 0

Reorder the terms:
(7 + -1w)(-1 + 2w) = 0

Multiply (7 + -1w) * (-1 + 2w)
(7(-1 + 2w) + -1w * (-1 + 2w)) = 0
((-1 * 7 + 2w * 7) + -1w * (-1 + 2w)) = 0
((-7 + 14w) + -1w * (-1 + 2w)) = 0
(-7 + 14w + (-1 * -1w + 2w * -1w)) = 0
(-7 + 14w + (1w + -2w2)) = 0

Combine like terms: 14w + 1w = 15w
(-7 + 15w + -2w2) = 0

Solving
-7 + 15w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-7 + w)(1 + -2w) = 0


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

Simplifying
-7 + w = 0

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

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

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

Simplifying
w = 7

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

Simplifying
1 + -2w = 0

Solving
1 + -2w = 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 + -2w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2w = 0 + -1
-2w = 0 + -1

Combine like terms: 0 + -1 = -1
-2w = -1

Divide each side by '-2'.
w = 0.5

Simplifying
w = 0.5
Solution
w = {7, 0.5}

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