(y-5)(y-5)=2y^2-14y+4

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Solution for (y-5)(y-5)=2y^2-14y+4 equation: 


Simplifying
(y + -5)(y + -5) = 2y2 + -14y + 4

Reorder the terms:
(-5 + y)(y + -5) = 2y2 + -14y + 4

Reorder the terms:
(-5 + y)(-5 + y) = 2y2 + -14y + 4

Multiply (-5 + y) * (-5 + y)
(-5(-5 + y) + y(-5 + y)) = 2y2 + -14y + 4
((-5 * -5 + y * -5) + y(-5 + y)) = 2y2 + -14y + 4
((25 + -5y) + y(-5 + y)) = 2y2 + -14y + 4
(25 + -5y + (-5 * y + y * y)) = 2y2 + -14y + 4
(25 + -5y + (-5y + y2)) = 2y2 + -14y + 4

Combine like terms: -5y + -5y = -10y
(25 + -10y + y2) = 2y2 + -14y + 4

Reorder the terms:
25 + -10y + y2 = 4 + -14y + 2y2

Solving
25 + -10y + y2 = 4 + -14y + 2y2

Solving for variable 'y'.

Reorder the terms:
25 + -4 + -10y + 14y + y2 + -2y2 = 4 + -14y + 2y2 + -4 + 14y + -2y2

Combine like terms: 25 + -4 = 21
21 + -10y + 14y + y2 + -2y2 = 4 + -14y + 2y2 + -4 + 14y + -2y2

Combine like terms: -10y + 14y = 4y
21 + 4y + y2 + -2y2 = 4 + -14y + 2y2 + -4 + 14y + -2y2

Combine like terms: y2 + -2y2 = -1y2
21 + 4y + -1y2 = 4 + -14y + 2y2 + -4 + 14y + -2y2

Reorder the terms:
21 + 4y + -1y2 = 4 + -4 + -14y + 14y + 2y2 + -2y2

Combine like terms: 4 + -4 = 0
21 + 4y + -1y2 = 0 + -14y + 14y + 2y2 + -2y2
21 + 4y + -1y2 = -14y + 14y + 2y2 + -2y2

Combine like terms: -14y + 14y = 0
21 + 4y + -1y2 = 0 + 2y2 + -2y2
21 + 4y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
21 + 4y + -1y2 = 0

Factor a trinomial.
(7 + -1y)(3 + y) = 0


Subproblem 1
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 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 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7

Subproblem 2
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

Add '-3' to each side of the equation.
3 + -3 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

Simplifying
y = -3
Solution
y = {7, -3}

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