(y-1)(2y-4)=0

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Solution for (y-1)(2y-4)=0 equation:


Simplifying
(y + -1)(2y + -4) = 0

Reorder the terms:
(-1 + y)(2y + -4) = 0

Reorder the terms:
(-1 + y)(-4 + 2y) = 0

Multiply (-1 + y) * (-4 + 2y)
(-1(-4 + 2y) + y(-4 + 2y)) = 0
((-4 * -1 + 2y * -1) + y(-4 + 2y)) = 0
((4 + -2y) + y(-4 + 2y)) = 0
(4 + -2y + (-4 * y + 2y * y)) = 0
(4 + -2y + (-4y + 2y2)) = 0

Combine like terms: -2y + -4y = -6y
(4 + -6y + 2y2) = 0

Solving
4 + -6y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -3y + y2) = 0

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

Ignore the factor 2.

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 '(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 = {1, 2}

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