y^2=15y-54

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Solution for y^2=15y-54 equation:


Simplifying
y2 = 15y + -54

Reorder the terms:
y2 = -54 + 15y

Solving
y2 = -54 + 15y

Solving for variable 'y'.

Reorder the terms:
54 + -15y + y2 = -54 + 15y + 54 + -15y

Reorder the terms:
54 + -15y + y2 = -54 + 54 + 15y + -15y

Combine like terms: -54 + 54 = 0
54 + -15y + y2 = 0 + 15y + -15y
54 + -15y + y2 = 15y + -15y

Combine like terms: 15y + -15y = 0
54 + -15y + y2 = 0

Factor a trinomial.
(6 + -1y)(9 + -1y) = 0

Subproblem 1

Set the factor '(6 + -1y)' equal to zero and attempt to solve: Simplifying 6 + -1y = 0 Solving 6 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1y = 0 + -6 -1y = 0 + -6 Combine like terms: 0 + -6 = -6 -1y = -6 Divide each side by '-1'. y = 6 Simplifying y = 6

Subproblem 2

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

Solution

y = {6, 9}

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