3y=2y(y+12)

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Solution for 3y=2y(y+12) equation:


Simplifying
3y = 2y(y + 12)

Reorder the terms:
3y = 2y(12 + y)
3y = (12 * 2y + y * 2y)
3y = (24y + 2y2)

Solving
3y = 24y + 2y2

Solving for variable 'y'.

Combine like terms: 3y + -24y = -21y
-21y + -2y2 = 24y + 2y2 + -24y + -2y2

Reorder the terms:
-21y + -2y2 = 24y + -24y + 2y2 + -2y2

Combine like terms: 24y + -24y = 0
-21y + -2y2 = 0 + 2y2 + -2y2
-21y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-21y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '-1y'.
-1y(21 + 2y) = 0

Ignore the factor -1.

Subproblem 1

Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0

Subproblem 2

Set the factor '(21 + 2y)' equal to zero and attempt to solve: Simplifying 21 + 2y = 0 Solving 21 + 2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + 2y = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 2y = 0 + -21 2y = 0 + -21 Combine like terms: 0 + -21 = -21 2y = -21 Divide each side by '2'. y = -10.5 Simplifying y = -10.5

Solution

y = {0, -10.5}

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