10y^2-17y+12=y+16

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Solution for 10y^2-17y+12=y+16 equation: 


Simplifying
10y2 + -17y + 12 = y + 16

Reorder the terms:
12 + -17y + 10y2 = y + 16

Reorder the terms:
12 + -17y + 10y2 = 16 + y

Solving
12 + -17y + 10y2 = 16 + y

Solving for variable 'y'.

Reorder the terms:
12 + -16 + -17y + -1y + 10y2 = 16 + y + -16 + -1y

Combine like terms: 12 + -16 = -4
-4 + -17y + -1y + 10y2 = 16 + y + -16 + -1y

Combine like terms: -17y + -1y = -18y
-4 + -18y + 10y2 = 16 + y + -16 + -1y

Reorder the terms:
-4 + -18y + 10y2 = 16 + -16 + y + -1y

Combine like terms: 16 + -16 = 0
-4 + -18y + 10y2 = 0 + y + -1y
-4 + -18y + 10y2 = y + -1y

Combine like terms: y + -1y = 0
-4 + -18y + 10y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -9y + 5y2) = 0

Factor a trinomial.
2((-1 + -5y)(2 + -1y)) = 0

Ignore the factor 2.

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

Simplifying
-1 + -5y = 0

Solving
-1 + -5y = 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 + -5y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5y = 0 + 1
-5y = 0 + 1

Combine like terms: 0 + 1 = 1
-5y = 1

Divide each side by '-5'.
y = -0.2

Simplifying
y = -0.2

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-0.2, 2}

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