y^2-10y+25=2y^2-20y+46

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Solution for y^2-10y+25=2y^2-20y+46 equation: 


Simplifying
y2 + -10y + 25 = 2y2 + -20y + 46

Reorder the terms:
25 + -10y + y2 = 2y2 + -20y + 46

Reorder the terms:
25 + -10y + y2 = 46 + -20y + 2y2

Solving
25 + -10y + y2 = 46 + -20y + 2y2

Solving for variable 'y'.

Reorder the terms:
25 + -46 + -10y + 20y + y2 + -2y2 = 46 + -20y + 2y2 + -46 + 20y + -2y2

Combine like terms: 25 + -46 = -21
-21 + -10y + 20y + y2 + -2y2 = 46 + -20y + 2y2 + -46 + 20y + -2y2

Combine like terms: -10y + 20y = 10y
-21 + 10y + y2 + -2y2 = 46 + -20y + 2y2 + -46 + 20y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-21 + 10y + -1y2 = 46 + -20y + 2y2 + -46 + 20y + -2y2

Reorder the terms:
-21 + 10y + -1y2 = 46 + -46 + -20y + 20y + 2y2 + -2y2

Combine like terms: 46 + -46 = 0
-21 + 10y + -1y2 = 0 + -20y + 20y + 2y2 + -2y2
-21 + 10y + -1y2 = -20y + 20y + 2y2 + -2y2

Combine like terms: -20y + 20y = 0
-21 + 10y + -1y2 = 0 + 2y2 + -2y2
-21 + 10y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-21 + 10y + -1y2 = 0

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


Subproblem 1
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

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

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

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

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