0=5y^2-5y-30

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Solution for 0=5y^2-5y-30 equation: 


Simplifying
0 = 5y2 + -5y + -30

Reorder the terms:
0 = -30 + -5y + 5y2

Solving
0 = -30 + -5y + 5y2

Solving for variable 'y'.

Combine like terms: 0 + 30 = 30
30 + 5y + -5y2 = -30 + -5y + 5y2 + 30 + 5y + -5y2

Reorder the terms:
30 + 5y + -5y2 = -30 + 30 + -5y + 5y + 5y2 + -5y2

Combine like terms: -30 + 30 = 0
30 + 5y + -5y2 = 0 + -5y + 5y + 5y2 + -5y2
30 + 5y + -5y2 = -5y + 5y + 5y2 + -5y2

Combine like terms: -5y + 5y = 0
30 + 5y + -5y2 = 0 + 5y2 + -5y2
30 + 5y + -5y2 = 5y2 + -5y2

Combine like terms: 5y2 + -5y2 = 0
30 + 5y + -5y2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + y + -1y2) = 0

Factor a trinomial.
5((3 + -1y)(2 + y)) = 0

Ignore the factor 5.

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

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3

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

Simplifying
2 + y = 0

Solving
2 + y = 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 + y = 0 + -2

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

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

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

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