3(y+9)1y=30

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Solution for 3(y+9)1y=30 equation:


Simplifying
3(y + 9) * 1y = 30

Reorder the terms:
3(9 + y) * 1y = 30

Reorder the terms for easier multiplication:
3 * 1y(9 + y) = 30

Multiply 3 * 1
3y(9 + y) = 30
(9 * 3y + y * 3y) = 30
(27y + 3y2) = 30

Solving
27y + 3y2 = 30

Solving for variable 'y'.

Reorder the terms:
-30 + 27y + 3y2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 27y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + 9y + y2) = 0

Factor a trinomial.
3((-10 + -1y)(1 + -1y)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-10 + -1y)' equal to zero and attempt to solve: Simplifying -10 + -1y = 0 Solving -10 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1y = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1y = 0 + 10 -1y = 0 + 10 Combine like terms: 0 + 10 = 10 -1y = 10 Divide each side by '-1'. y = -10 Simplifying y = -10

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 = {-10, 1}

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