Y=4Y^2-32Y+65

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Solution for Y=4Y^2-32Y+65 equation: 


Simplifying
Y = 4Y2 + -32Y + 65

Reorder the terms:
Y = 65 + -32Y + 4Y2

Solving
Y = 65 + -32Y + 4Y2

Solving for variable 'Y'.

Reorder the terms:
-65 + Y + 32Y + -4Y2 = 65 + -32Y + 4Y2 + -65 + 32Y + -4Y2

Combine like terms: Y + 32Y = 33Y
-65 + 33Y + -4Y2 = 65 + -32Y + 4Y2 + -65 + 32Y + -4Y2

Reorder the terms:
-65 + 33Y + -4Y2 = 65 + -65 + -32Y + 32Y + 4Y2 + -4Y2

Combine like terms: 65 + -65 = 0
-65 + 33Y + -4Y2 = 0 + -32Y + 32Y + 4Y2 + -4Y2
-65 + 33Y + -4Y2 = -32Y + 32Y + 4Y2 + -4Y2

Combine like terms: -32Y + 32Y = 0
-65 + 33Y + -4Y2 = 0 + 4Y2 + -4Y2
-65 + 33Y + -4Y2 = 4Y2 + -4Y2

Combine like terms: 4Y2 + -4Y2 = 0
-65 + 33Y + -4Y2 = 0

Factor a trinomial.
(-5 + Y)(13 + -4Y) = 0


Subproblem 1
Set the factor '(-5 + Y)' equal to zero and attempt to solve:

Simplifying
-5 + Y = 0

Solving
-5 + Y = 0

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

Add '5' to each side of the equation.
-5 + 5 + Y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + Y = 0 + 5
Y = 0 + 5

Combine like terms: 0 + 5 = 5
Y = 5

Simplifying
Y = 5

Subproblem 2
Set the factor '(13 + -4Y)' equal to zero and attempt to solve:

Simplifying
13 + -4Y = 0

Solving
13 + -4Y = 0

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

Add '-13' to each side of the equation.
13 + -13 + -4Y = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -4Y = 0 + -13
-4Y = 0 + -13

Combine like terms: 0 + -13 = -13
-4Y = -13

Divide each side by '-4'.
Y = 3.25

Simplifying
Y = 3.25
Solution
Y = {5, 3.25}

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