(5y-7)(y-1)=3

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Solution for (5y-7)(y-1)=3 equation:


Simplifying
(5y + -7)(y + -1) = 3

Reorder the terms:
(-7 + 5y)(y + -1) = 3

Reorder the terms:
(-7 + 5y)(-1 + y) = 3

Multiply (-7 + 5y) * (-1 + y)
(-7(-1 + y) + 5y * (-1 + y)) = 3
((-1 * -7 + y * -7) + 5y * (-1 + y)) = 3
((7 + -7y) + 5y * (-1 + y)) = 3
(7 + -7y + (-1 * 5y + y * 5y)) = 3
(7 + -7y + (-5y + 5y2)) = 3

Combine like terms: -7y + -5y = -12y
(7 + -12y + 5y2) = 3

Solving
7 + -12y + 5y2 = 3

Solving for variable 'y'.

Reorder the terms:
7 + -3 + -12y + 5y2 = 3 + -3

Combine like terms: 7 + -3 = 4
4 + -12y + 5y2 = 3 + -3

Combine like terms: 3 + -3 = 0
4 + -12y + 5y2 = 0

Factor a trinomial.
(2 + -5y)(2 + -1y) = 0

Subproblem 1

Set the factor '(2 + -5y)' equal to zero and attempt to solve: Simplifying 2 + -5y = 0 Solving 2 + -5y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5y = 0 + -2 -5y = 0 + -2 Combine like terms: 0 + -2 = -2 -5y = -2 Divide each side by '-5'. y = 0.4 Simplifying y = 0.4

Subproblem 2

Set the factor '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2

Solution

y = {0.4, 2}

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