11y-15=(y+5)(y-3)

Solution for 11y-15=(y+5)(y-3) equation:

Simplifying
11y + -15 = (y + 5)(y + -3)

Reorder the terms:
-15 + 11y = (y + 5)(y + -3)

Reorder the terms:
-15 + 11y = (5 + y)(y + -3)

Reorder the terms:
-15 + 11y = (5 + y)(-3 + y)

Multiply (5 + y) * (-3 + y)
-15 + 11y = (5(-3 + y) + y(-3 + y))
-15 + 11y = ((-3 * 5 + y * 5) + y(-3 + y))
-15 + 11y = ((-15 + 5y) + y(-3 + y))
-15 + 11y = (-15 + 5y + (-3 * y + y * y))
-15 + 11y = (-15 + 5y + (-3y + y2))

Combine like terms: 5y + -3y = 2y
-15 + 11y = (-15 + 2y + y2)

Add '15' to each side of the equation.
-15 + 15 + 11y = -15 + 2y + 15 + y2

Combine like terms: -15 + 15 = 0
0 + 11y = -15 + 2y + 15 + y2
11y = -15 + 2y + 15 + y2

Reorder the terms:
11y = -15 + 15 + 2y + y2

Combine like terms: -15 + 15 = 0
11y = 0 + 2y + y2
11y = 2y + y2

Solving
11y = 2y + y2

Solving for variable 'y'.

Combine like terms: 11y + -2y = 9y
9y + -1y2 = 2y + y2 + -2y + -1y2

Reorder the terms:
9y + -1y2 = 2y + -2y + y2 + -1y2

Combine like terms: 2y + -2y = 0
9y + -1y2 = 0 + y2 + -1y2
9y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
9y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(9 + -1y) = 0

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 '(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 = {0, 9}