(y-5)(y-5)=2y^2-4y+18

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Solution for (y-5)(y-5)=2y^2-4y+18 equation: 


Simplifying
(y + -5)(y + -5) = 2y2 + -4y + 18

Reorder the terms:
(-5 + y)(y + -5) = 2y2 + -4y + 18

Reorder the terms:
(-5 + y)(-5 + y) = 2y2 + -4y + 18

Multiply (-5 + y) * (-5 + y)
(-5(-5 + y) + y(-5 + y)) = 2y2 + -4y + 18
((-5 * -5 + y * -5) + y(-5 + y)) = 2y2 + -4y + 18
((25 + -5y) + y(-5 + y)) = 2y2 + -4y + 18
(25 + -5y + (-5 * y + y * y)) = 2y2 + -4y + 18
(25 + -5y + (-5y + y2)) = 2y2 + -4y + 18

Combine like terms: -5y + -5y = -10y
(25 + -10y + y2) = 2y2 + -4y + 18

Reorder the terms:
25 + -10y + y2 = 18 + -4y + 2y2

Solving
25 + -10y + y2 = 18 + -4y + 2y2

Solving for variable 'y'.

Reorder the terms:
25 + -18 + -10y + 4y + y2 + -2y2 = 18 + -4y + 2y2 + -18 + 4y + -2y2

Combine like terms: 25 + -18 = 7
7 + -10y + 4y + y2 + -2y2 = 18 + -4y + 2y2 + -18 + 4y + -2y2

Combine like terms: -10y + 4y = -6y
7 + -6y + y2 + -2y2 = 18 + -4y + 2y2 + -18 + 4y + -2y2

Combine like terms: y2 + -2y2 = -1y2
7 + -6y + -1y2 = 18 + -4y + 2y2 + -18 + 4y + -2y2

Reorder the terms:
7 + -6y + -1y2 = 18 + -18 + -4y + 4y + 2y2 + -2y2

Combine like terms: 18 + -18 = 0
7 + -6y + -1y2 = 0 + -4y + 4y + 2y2 + -2y2
7 + -6y + -1y2 = -4y + 4y + 2y2 + -2y2

Combine like terms: -4y + 4y = 0
7 + -6y + -1y2 = 0 + 2y2 + -2y2
7 + -6y + -1y2 = 2y2 + -2y2

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

Factor a trinomial.
(1 + -1y)(7 + y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + y)' equal to zero and attempt to solve:

Simplifying
7 + y = 0

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

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

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

Simplifying
y = -7
Solution
y = {1, -7}

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