(y(8y+10))=30378

Solution for (y(8y+10))=30378 equation:

Simplifying
(y(8y + 10)) = 30378

Reorder the terms:
(y(10 + 8y)) = 30378
((10 * y + 8y * y)) = 30378
((10y + 8y2)) = 30378
(10y + 8y2) = 30378

Remove parenthesis around (10y + 8y2)
10y + 8y2 = 30378

Solving
10y + 8y2 = 30378

Solving for variable 'y'.

Reorder the terms:
-30378 + 10y + 8y2 = 30378 + -30378

Combine like terms: 30378 + -30378 = 0
-30378 + 10y + 8y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15189 + 5y + 4y2) = 0

Factor a trinomial.
2((-249 + -4y)(61 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-249 + -4y)' equal to zero and attempt to solve:

Simplifying
-249 + -4y = 0

Solving
-249 + -4y = 0

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

Add '249' to each side of the equation.
-249 + 249 + -4y = 0 + 249

Combine like terms: -249 + 249 = 0
0 + -4y = 0 + 249
-4y = 0 + 249

Combine like terms: 0 + 249 = 249
-4y = 249

Divide each side by '-4'.
y = -62.25

Simplifying
y = -62.25
Subproblem 2
Set the factor '(61 + -1y)' equal to zero and attempt to solve:

Simplifying
61 + -1y = 0

Solving
61 + -1y = 0

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

Add '-61' to each side of the equation.
61 + -61 + -1y = 0 + -61

Combine like terms: 61 + -61 = 0
0 + -1y = 0 + -61
-1y = 0 + -61

Combine like terms: 0 + -61 = -61
-1y = -61

Divide each side by '-1'.
y = 61

Simplifying
y = 61
Solution
y = {-62.25, 61}