10y^2=-61y+462

Solution for 10y^2=-61y+462 equation:

Simplifying
10y2 = -61y + 462

Reorder the terms:
10y2 = 462 + -61y

Solving
10y2 = 462 + -61y

Solving for variable 'y'.

Reorder the terms:
-462 + 61y + 10y2 = 462 + -61y + -462 + 61y

Reorder the terms:
-462 + 61y + 10y2 = 462 + -462 + -61y + 61y

Combine like terms: 462 + -462 = 0
-462 + 61y + 10y2 = 0 + -61y + 61y
-462 + 61y + 10y2 = -61y + 61y

Combine like terms: -61y + 61y = 0
-462 + 61y + 10y2 = 0

Factor a trinomial.
(-21 + -2y)(22 + -5y) = 0

Subproblem 1
Set the factor '(-21 + -2y)' equal to zero and attempt to solve:

Simplifying
-21 + -2y = 0

Solving
-21 + -2y = 0

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

Add '21' to each side of the equation.
-21 + 21 + -2y = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -2y = 0 + 21
-2y = 0 + 21

Combine like terms: 0 + 21 = 21
-2y = 21

Divide each side by '-2'.
y = -10.5

Simplifying
y = -10.5
Subproblem 2
Set the factor '(22 + -5y)' equal to zero and attempt to solve:

Simplifying
22 + -5y = 0

Solving
22 + -5y = 0

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

Add '-22' to each side of the equation.
22 + -22 + -5y = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -5y = 0 + -22
-5y = 0 + -22

Combine like terms: 0 + -22 = -22
-5y = -22

Divide each side by '-5'.
y = 4.4

Simplifying
y = 4.4
Solution
y = {-10.5, 4.4}