(5y+1)(5y+1)=64

Solution for (5y+1)(5y+1)=64 equation:

Simplifying
(5y + 1)(5y + 1) = 64

Reorder the terms:
(1 + 5y)(5y + 1) = 64

Reorder the terms:
(1 + 5y)(1 + 5y) = 64

Multiply (1 + 5y) * (1 + 5y)
(1(1 + 5y) + 5y * (1 + 5y)) = 64
((1 * 1 + 5y * 1) + 5y * (1 + 5y)) = 64
((1 + 5y) + 5y * (1 + 5y)) = 64
(1 + 5y + (1 * 5y + 5y * 5y)) = 64
(1 + 5y + (5y + 25y2)) = 64

Combine like terms: 5y + 5y = 10y
(1 + 10y + 25y2) = 64

Solving
1 + 10y + 25y2 = 64

Solving for variable 'y'.

Reorder the terms:
1 + -64 + 10y + 25y2 = 64 + -64

Combine like terms: 1 + -64 = -63
-63 + 10y + 25y2 = 64 + -64

Combine like terms: 64 + -64 = 0
-63 + 10y + 25y2 = 0

Factor a trinomial.
(-9 + -5y)(7 + -5y) = 0

Subproblem 1
Set the factor '(-9 + -5y)' equal to zero and attempt to solve:

Simplifying
-9 + -5y = 0

Solving
-9 + -5y = 0

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

Add '9' to each side of the equation.
-9 + 9 + -5y = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -5y = 0 + 9
-5y = 0 + 9

Combine like terms: 0 + 9 = 9
-5y = 9

Divide each side by '-5'.
y = -1.8

Simplifying
y = -1.8
Subproblem 2
Set the factor '(7 + -5y)' equal to zero and attempt to solve:

Simplifying
7 + -5y = 0

Solving
7 + -5y = 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 + -5y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5y = 0 + -7
-5y = 0 + -7

Combine like terms: 0 + -7 = -7
-5y = -7

Divide each side by '-5'.
y = 1.4

Simplifying
y = 1.4
Solution
y = {-1.8, 1.4}