y^2-10y+25=3y-5

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Solution for y^2-10y+25=3y-5 equation: 


Simplifying
y2 + -10y + 25 = 3y + -5

Reorder the terms:
25 + -10y + y2 = 3y + -5

Reorder the terms:
25 + -10y + y2 = -5 + 3y

Solving
25 + -10y + y2 = -5 + 3y

Solving for variable 'y'.

Reorder the terms:
25 + 5 + -10y + -3y + y2 = -5 + 3y + 5 + -3y

Combine like terms: 25 + 5 = 30
30 + -10y + -3y + y2 = -5 + 3y + 5 + -3y

Combine like terms: -10y + -3y = -13y
30 + -13y + y2 = -5 + 3y + 5 + -3y

Reorder the terms:
30 + -13y + y2 = -5 + 5 + 3y + -3y

Combine like terms: -5 + 5 = 0
30 + -13y + y2 = 0 + 3y + -3y
30 + -13y + y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
30 + -13y + y2 = 0

Factor a trinomial.
(3 + -1y)(10 + -1y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(10 + -1y)' equal to zero and attempt to solve:

Simplifying
10 + -1y = 0

Solving
10 + -1y = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1y = 0 + -10
-1y = 0 + -10

Combine like terms: 0 + -10 = -10
-1y = -10

Divide each side by '-1'.
y = 10

Simplifying
y = 10
Solution
y = {3, 10}

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