(y-1)(y-1)=2y^2-9y+7

Solution for (y-1)(y-1)=2y^2-9y+7 equation:

Simplifying
(y + -1)(y + -1) = 2y2 + -9y + 7

Reorder the terms:
(-1 + y)(y + -1) = 2y2 + -9y + 7

Reorder the terms:
(-1 + y)(-1 + y) = 2y2 + -9y + 7

Multiply (-1 + y) * (-1 + y)
(-1(-1 + y) + y(-1 + y)) = 2y2 + -9y + 7
((-1 * -1 + y * -1) + y(-1 + y)) = 2y2 + -9y + 7
((1 + -1y) + y(-1 + y)) = 2y2 + -9y + 7
(1 + -1y + (-1 * y + y * y)) = 2y2 + -9y + 7
(1 + -1y + (-1y + y2)) = 2y2 + -9y + 7

Combine like terms: -1y + -1y = -2y
(1 + -2y + y2) = 2y2 + -9y + 7

Reorder the terms:
1 + -2y + y2 = 7 + -9y + 2y2

Solving
1 + -2y + y2 = 7 + -9y + 2y2

Solving for variable 'y'.

Reorder the terms:
1 + -7 + -2y + 9y + y2 + -2y2 = 7 + -9y + 2y2 + -7 + 9y + -2y2

Combine like terms: 1 + -7 = -6
-6 + -2y + 9y + y2 + -2y2 = 7 + -9y + 2y2 + -7 + 9y + -2y2

Combine like terms: -2y + 9y = 7y
-6 + 7y + y2 + -2y2 = 7 + -9y + 2y2 + -7 + 9y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-6 + 7y + -1y2 = 7 + -9y + 2y2 + -7 + 9y + -2y2

Reorder the terms:
-6 + 7y + -1y2 = 7 + -7 + -9y + 9y + 2y2 + -2y2

Combine like terms: 7 + -7 = 0
-6 + 7y + -1y2 = 0 + -9y + 9y + 2y2 + -2y2
-6 + 7y + -1y2 = -9y + 9y + 2y2 + -2y2

Combine like terms: -9y + 9y = 0
-6 + 7y + -1y2 = 0 + 2y2 + -2y2
-6 + 7y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-6 + 7y + -1y2 = 0

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

Subproblem 1
Set the factor '(-6 + y)' equal to zero and attempt to solve:

Simplifying
-6 + y = 0

Solving
-6 + y = 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 + y = 0 + 6

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

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

Simplifying
y = 6
Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

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

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

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

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

Simplifying
y = 1
Solution
y = {6, 1}