5y+15-30=(y-3)(y+3)

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Solution for 5y+15-30=(y-3)(y+3) equation: 


Simplifying
5y + 15 + -30 = (y + -3)(y + 3)

Reorder the terms:
15 + -30 + 5y = (y + -3)(y + 3)

Combine like terms: 15 + -30 = -15
-15 + 5y = (y + -3)(y + 3)

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

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

Multiply (-3 + y) * (3 + y)
-15 + 5y = (-3(3 + y) + y(3 + y))
-15 + 5y = ((3 * -3 + y * -3) + y(3 + y))
-15 + 5y = ((-9 + -3y) + y(3 + y))
-15 + 5y = (-9 + -3y + (3 * y + y * y))
-15 + 5y = (-9 + -3y + (3y + y2))

Combine like terms: -3y + 3y = 0
-15 + 5y = (-9 + 0 + y2)
-15 + 5y = (-9 + y2)

Solving
-15 + 5y = -9 + y2

Solving for variable 'y'.

Reorder the terms:
-15 + 9 + 5y + -1y2 = -9 + y2 + 9 + -1y2

Combine like terms: -15 + 9 = -6
-6 + 5y + -1y2 = -9 + y2 + 9 + -1y2

Reorder the terms:
-6 + 5y + -1y2 = -9 + 9 + y2 + -1y2

Combine like terms: -9 + 9 = 0
-6 + 5y + -1y2 = 0 + y2 + -1y2
-6 + 5y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-6 + 5y + -1y2 = 0

Factor a trinomial.
(-3 + y)(2 + -1y) = 0


Subproblem 1
Set the factor '(-3 + y)' equal to zero and attempt to solve:

Simplifying
-3 + y = 0

Solving
-3 + y = 0

Move all terms containing y to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + y = 0 + 3
y = 0 + 3

Combine like terms: 0 + 3 = 3
y = 3

Simplifying
y = 3

Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

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

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

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {3, 2}

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