(y-1)(y-3)=0

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Solution for (y-1)(y-3)=0 equation:


Simplifying
(y + -1)(y + -3) = 0

Reorder the terms:
(-1 + y)(y + -3) = 0

Reorder the terms:
(-1 + y)(-3 + y) = 0

Multiply (-1 + y) * (-3 + y)
(-1(-3 + y) + y(-3 + y)) = 0
((-3 * -1 + y * -1) + y(-3 + y)) = 0
((3 + -1y) + y(-3 + y)) = 0
(3 + -1y + (-3 * y + y * y)) = 0
(3 + -1y + (-3y + y2)) = 0

Combine like terms: -1y + -3y = -4y
(3 + -4y + y2) = 0

Solving
3 + -4y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(1 + -1y)(3 + -1y) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(3 + -1y)' equal to zero and attempt to solve: Simplifying 3 + -1y = 0 Solving 3 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1y = 0 + -3 -1y = 0 + -3 Combine like terms: 0 + -3 = -3 -1y = -3 Divide each side by '-1'. y = 3 Simplifying y = 3

Solution

y = {1, 3}

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