24y(5y+6)=27y+3

Solution for 24y(5y+6)=27y+3 equation:

Simplifying
24y(5y + 6) = 27y + 3

Reorder the terms:
24y(6 + 5y) = 27y + 3
(6 * 24y + 5y * 24y) = 27y + 3
(144y + 120y2) = 27y + 3

Reorder the terms:
144y + 120y2 = 3 + 27y

Solving
144y + 120y2 = 3 + 27y

Solving for variable 'y'.

Reorder the terms:
-3 + 144y + -27y + 120y2 = 3 + 27y + -3 + -27y

Combine like terms: 144y + -27y = 117y
-3 + 117y + 120y2 = 3 + 27y + -3 + -27y

Reorder the terms:
-3 + 117y + 120y2 = 3 + -3 + 27y + -27y

Combine like terms: 3 + -3 = 0
-3 + 117y + 120y2 = 0 + 27y + -27y
-3 + 117y + 120y2 = 27y + -27y

Combine like terms: 27y + -27y = 0
-3 + 117y + 120y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 39y + 40y2) = 0

Factor a trinomial.
3((-1 + -1y)(1 + -40y)) = 0

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

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 0

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

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

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

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

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

Simplifying
y = -1
Subproblem 2
Set the factor '(1 + -40y)' equal to zero and attempt to solve:

Simplifying
1 + -40y = 0

Solving
1 + -40y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -40y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -40y = 0 + -1
-40y = 0 + -1

Combine like terms: 0 + -1 = -1
-40y = -1

Divide each side by '-40'.
y = 0.025

Simplifying
y = 0.025
Solution
y = {-1, 0.025}