6y(7y+6)=5(13y+1)

Solution for 6y(7y+6)=5(13y+1) equation:

Simplifying
6y(7y + 6) = 5(13y + 1)

Reorder the terms:
6y(6 + 7y) = 5(13y + 1)
(6 * 6y + 7y * 6y) = 5(13y + 1)
(36y + 42y2) = 5(13y + 1)

Reorder the terms:
36y + 42y2 = 5(1 + 13y)
36y + 42y2 = (1 * 5 + 13y * 5)
36y + 42y2 = (5 + 65y)

Solving
36y + 42y2 = 5 + 65y

Solving for variable 'y'.

Reorder the terms:
-5 + 36y + -65y + 42y2 = 5 + 65y + -5 + -65y

Combine like terms: 36y + -65y = -29y
-5 + -29y + 42y2 = 5 + 65y + -5 + -65y

Reorder the terms:
-5 + -29y + 42y2 = 5 + -5 + 65y + -65y

Combine like terms: 5 + -5 = 0
-5 + -29y + 42y2 = 0 + 65y + -65y
-5 + -29y + 42y2 = 65y + -65y

Combine like terms: 65y + -65y = 0
-5 + -29y + 42y2 = 0

Factor a trinomial.
(-1 + -7y)(5 + -6y) = 0

Subproblem 1
Set the factor '(-1 + -7y)' equal to zero and attempt to solve:

Simplifying
-1 + -7y = 0

Solving
-1 + -7y = 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 + -7y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7y = 0 + 1
-7y = 0 + 1

Combine like terms: 0 + 1 = 1
-7y = 1

Divide each side by '-7'.
y = -0.1428571429

Simplifying
y = -0.1428571429
Subproblem 2
Set the factor '(5 + -6y)' equal to zero and attempt to solve:

Simplifying
5 + -6y = 0

Solving
5 + -6y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6y = 0 + -5
-6y = 0 + -5

Combine like terms: 0 + -5 = -5
-6y = -5

Divide each side by '-6'.
y = 0.8333333333

Simplifying
y = 0.8333333333
Solution
y = {-0.1428571429, 0.8333333333}