(y+1)(y+1)=8y-7

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Solution for (y+1)(y+1)=8y-7 equation: 


Simplifying
(y + 1)(y + 1) = 8y + -7

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

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

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

Combine like terms: 1y + 1y = 2y
(1 + 2y + y2) = 8y + -7

Reorder the terms:
1 + 2y + y2 = -7 + 8y

Solving
1 + 2y + y2 = -7 + 8y

Solving for variable 'y'.

Reorder the terms:
1 + 7 + 2y + -8y + y2 = -7 + 8y + 7 + -8y

Combine like terms: 1 + 7 = 8
8 + 2y + -8y + y2 = -7 + 8y + 7 + -8y

Combine like terms: 2y + -8y = -6y
8 + -6y + y2 = -7 + 8y + 7 + -8y

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

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

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

Factor a trinomial.
(2 + -1y)(4 + -1y) = 0


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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2

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

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {2, 4}

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