(2y+6)(y-1)=0

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Solution for (2y+6)(y-1)=0 equation:


Simplifying
(2y + 6)(y + -1) = 0

Reorder the terms:
(6 + 2y)(y + -1) = 0

Reorder the terms:
(6 + 2y)(-1 + y) = 0

Multiply (6 + 2y) * (-1 + y)
(6(-1 + y) + 2y * (-1 + y)) = 0
((-1 * 6 + y * 6) + 2y * (-1 + y)) = 0
((-6 + 6y) + 2y * (-1 + y)) = 0
(-6 + 6y + (-1 * 2y + y * 2y)) = 0
(-6 + 6y + (-2y + 2y2)) = 0

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

Solving
-6 + 4y + 2y2 = 0

Solving for variable 'y'.

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

Factor a trinomial.
2((-3 + -1y)(1 + -1y)) = 0

Ignore the factor 2.

Subproblem 1

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

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, 1}

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