(3y+1)-8=(y+1)(8y-1)

Solution for (3y+1)-8=(y+1)(8y-1) equation:

Simplifying
(3y + 1) + -8 = (y + 1)(8y + -1)

Reorder the terms:
(1 + 3y) + -8 = (y + 1)(8y + -1)

Remove parenthesis around (1 + 3y)
1 + 3y + -8 = (y + 1)(8y + -1)

Reorder the terms:
1 + -8 + 3y = (y + 1)(8y + -1)

Combine like terms: 1 + -8 = -7
-7 + 3y = (y + 1)(8y + -1)

Reorder the terms:
-7 + 3y = (1 + y)(8y + -1)

Reorder the terms:
-7 + 3y = (1 + y)(-1 + 8y)

Multiply (1 + y) * (-1 + 8y)
-7 + 3y = (1(-1 + 8y) + y(-1 + 8y))
-7 + 3y = ((-1 * 1 + 8y * 1) + y(-1 + 8y))
-7 + 3y = ((-1 + 8y) + y(-1 + 8y))
-7 + 3y = (-1 + 8y + (-1 * y + 8y * y))
-7 + 3y = (-1 + 8y + (-1y + 8y2))

Combine like terms: 8y + -1y = 7y
-7 + 3y = (-1 + 7y + 8y2)

Solving
-7 + 3y = -1 + 7y + 8y2

Solving for variable 'y'.

Reorder the terms:
-7 + 1 + 3y + -7y + -8y2 = -1 + 7y + 8y2 + 1 + -7y + -8y2

Combine like terms: -7 + 1 = -6
-6 + 3y + -7y + -8y2 = -1 + 7y + 8y2 + 1 + -7y + -8y2

Combine like terms: 3y + -7y = -4y
-6 + -4y + -8y2 = -1 + 7y + 8y2 + 1 + -7y + -8y2

Reorder the terms:
-6 + -4y + -8y2 = -1 + 1 + 7y + -7y + 8y2 + -8y2

Combine like terms: -1 + 1 = 0
-6 + -4y + -8y2 = 0 + 7y + -7y + 8y2 + -8y2
-6 + -4y + -8y2 = 7y + -7y + 8y2 + -8y2

Combine like terms: 7y + -7y = 0
-6 + -4y + -8y2 = 0 + 8y2 + -8y2
-6 + -4y + -8y2 = 8y2 + -8y2

Combine like terms: 8y2 + -8y2 = 0
-6 + -4y + -8y2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 2y + 4y2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(3 + 2y + 4y2)' equal to zero and attempt to solve:

Simplifying
3 + 2y + 4y2 = 0

Solving
3 + 2y + 4y2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
0.75 + 0.5y + y2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 0.5y + -0.75 + y2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 0.5y + y2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 0.5y + y2 = 0 + -0.75
0.5y + y2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
0.5y + y2 = -0.75

The y term is 0.5y.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5y + 0.0625 + y2 = -0.75 + 0.0625

Reorder the terms:
0.0625 + 0.5y + y2 = -0.75 + 0.0625

Combine like terms: -0.75 + 0.0625 = -0.6875
0.0625 + 0.5y + y2 = -0.6875

Factor a perfect square on the left side:
(y + 0.25)(y + 0.25) = -0.6875

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.