5y(8y+13)=6(13y+7)

Solution for 5y(8y+13)=6(13y+7) equation:

Simplifying
5y(8y + 13) = 6(13y + 7)

Reorder the terms:
5y(13 + 8y) = 6(13y + 7)
(13 * 5y + 8y * 5y) = 6(13y + 7)
(65y + 40y2) = 6(13y + 7)

Reorder the terms:
65y + 40y2 = 6(7 + 13y)
65y + 40y2 = (7 * 6 + 13y * 6)
65y + 40y2 = (42 + 78y)

Solving
65y + 40y2 = 42 + 78y

Solving for variable 'y'.

Reorder the terms:
-42 + 65y + -78y + 40y2 = 42 + 78y + -42 + -78y

Combine like terms: 65y + -78y = -13y
-42 + -13y + 40y2 = 42 + 78y + -42 + -78y

Reorder the terms:
-42 + -13y + 40y2 = 42 + -42 + 78y + -78y

Combine like terms: 42 + -42 = 0
-42 + -13y + 40y2 = 0 + 78y + -78y
-42 + -13y + 40y2 = 78y + -78y

Combine like terms: 78y + -78y = 0
-42 + -13y + 40y2 = 0

Factor a trinomial.
(-7 + -8y)(6 + -5y) = 0

Subproblem 1
Set the factor '(-7 + -8y)' equal to zero and attempt to solve:

Simplifying
-7 + -8y = 0

Solving
-7 + -8y = 0

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

Add '7' to each side of the equation.
-7 + 7 + -8y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -8y = 0 + 7
-8y = 0 + 7

Combine like terms: 0 + 7 = 7
-8y = 7

Divide each side by '-8'.
y = -0.875

Simplifying
y = -0.875
Subproblem 2
Set the factor '(6 + -5y)' equal to zero and attempt to solve:

Simplifying
6 + -5y = 0

Solving
6 + -5y = 0

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

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

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

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

Divide each side by '-5'.
y = 1.2

Simplifying
y = 1.2
Solution
y = {-0.875, 1.2}