(9-Y)(3Y+1)=0

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Solution for (9-Y)(3Y+1)=0 equation:


Simplifying
(9 + -1Y)(3Y + 1) = 0

Reorder the terms:
(9 + -1Y)(1 + 3Y) = 0

Multiply (9 + -1Y) * (1 + 3Y)
(9(1 + 3Y) + -1Y * (1 + 3Y)) = 0
((1 * 9 + 3Y * 9) + -1Y * (1 + 3Y)) = 0
((9 + 27Y) + -1Y * (1 + 3Y)) = 0
(9 + 27Y + (1 * -1Y + 3Y * -1Y)) = 0
(9 + 27Y + (-1Y + -3Y2)) = 0

Combine like terms: 27Y + -1Y = 26Y
(9 + 26Y + -3Y2) = 0

Solving
9 + 26Y + -3Y2 = 0

Solving for variable 'Y'.

Factor a trinomial.
(9 + -1Y)(1 + 3Y) = 0

Subproblem 1

Set the factor '(9 + -1Y)' equal to zero and attempt to solve: Simplifying 9 + -1Y = 0 Solving 9 + -1Y = 0 Move all terms containing Y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1Y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1Y = 0 + -9 -1Y = 0 + -9 Combine like terms: 0 + -9 = -9 -1Y = -9 Divide each side by '-1'. Y = 9 Simplifying Y = 9

Subproblem 2

Set the factor '(1 + 3Y)' equal to zero and attempt to solve: Simplifying 1 + 3Y = 0 Solving 1 + 3Y = 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 + 3Y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3Y = 0 + -1 3Y = 0 + -1 Combine like terms: 0 + -1 = -1 3Y = -1 Divide each side by '3'. Y = -0.3333333333 Simplifying Y = -0.3333333333

Solution

Y = {9, -0.3333333333}

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