5(y^2-42)=-61y

Solution for 5(y^2-42)=-61y equation:

Simplifying
5(y2 + -42) = -61y

Reorder the terms:
5(-42 + y2) = -61y
(-42 * 5 + y2 * 5) = -61y
(-210 + 5y2) = -61y

Solving
-210 + 5y2 = -61y

Solving for variable 'y'.

Reorder the terms:
-210 + 61y + 5y2 = -61y + 61y

Combine like terms: -61y + 61y = 0
-210 + 61y + 5y2 = 0

Factor a trinomial.
(-15 + -1y)(14 + -5y) = 0

Subproblem 1
Set the factor '(-15 + -1y)' equal to zero and attempt to solve:

Simplifying
-15 + -1y = 0

Solving
-15 + -1y = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1y = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1y = 0 + 15
-1y = 0 + 15

Combine like terms: 0 + 15 = 15
-1y = 15

Divide each side by '-1'.
y = -15

Simplifying
y = -15
Subproblem 2
Set the factor '(14 + -5y)' equal to zero and attempt to solve:

Simplifying
14 + -5y = 0

Solving
14 + -5y = 0

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

Add '-14' to each side of the equation.
14 + -14 + -5y = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -5y = 0 + -14
-5y = 0 + -14

Combine like terms: 0 + -14 = -14
-5y = -14

Divide each side by '-5'.
y = 2.8

Simplifying
y = 2.8
Solution
y = {-15, 2.8}