3y^2-y-30=(3y-10)

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Solution for 3y^2-y-30=(3y-10) equation: 


Simplifying
3y2 + -1y + -30 = (3y + -10)

Reorder the terms:
-30 + -1y + 3y2 = (3y + -10)

Reorder the terms:
-30 + -1y + 3y2 = (-10 + 3y)

Remove parenthesis around (-10 + 3y)
-30 + -1y + 3y2 = -10 + 3y

Solving
-30 + -1y + 3y2 = -10 + 3y

Solving for variable 'y'.

Reorder the terms:
-30 + 10 + -1y + -3y + 3y2 = -10 + 3y + 10 + -3y

Combine like terms: -30 + 10 = -20
-20 + -1y + -3y + 3y2 = -10 + 3y + 10 + -3y

Combine like terms: -1y + -3y = -4y
-20 + -4y + 3y2 = -10 + 3y + 10 + -3y

Reorder the terms:
-20 + -4y + 3y2 = -10 + 10 + 3y + -3y

Combine like terms: -10 + 10 = 0
-20 + -4y + 3y2 = 0 + 3y + -3y
-20 + -4y + 3y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-20 + -4y + 3y2 = 0

Factor a trinomial.
(-2 + -1y)(10 + -3y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(10 + -3y)' equal to zero and attempt to solve:

Simplifying
10 + -3y = 0

Solving
10 + -3y = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3y = 0 + -10
-3y = 0 + -10

Combine like terms: 0 + -10 = -10
-3y = -10

Divide each side by '-3'.
y = 3.333333333

Simplifying
y = 3.333333333
Solution
y = {-2, 3.333333333}

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