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

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


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

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

Multiply (-7 + 2y) * (1 + -1y)
(-7(1 + -1y) + 2y * (1 + -1y)) = 0
((1 * -7 + -1y * -7) + 2y * (1 + -1y)) = 0
((-7 + 7y) + 2y * (1 + -1y)) = 0
(-7 + 7y + (1 * 2y + -1y * 2y)) = 0
(-7 + 7y + (2y + -2y2)) = 0

Combine like terms: 7y + 2y = 9y
(-7 + 9y + -2y2) = 0

Solving
-7 + 9y + -2y2 = 0

Solving for variable 'y'.

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

Subproblem 1

Set the factor '(-7 + 2y)' equal to zero and attempt to solve: Simplifying -7 + 2y = 0 Solving -7 + 2y = 0 Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 2y = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2y = 0 + 7 2y = 0 + 7 Combine like terms: 0 + 7 = 7 2y = 7 Divide each side by '2'. y = 3.5 Simplifying y = 3.5

Subproblem 2

Set the factor '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1

Solution

y = {3.5, 1}

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