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

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

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

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

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

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

Solving for variable 'y'.

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

Combine like terms: 12 + -10 = 2
2 + -17y + -1y + 10y2 = 10 + y + -10 + -1y

Combine like terms: -17y + -1y = -18y
2 + -18y + 10y2 = 10 + y + -10 + -1y

Reorder the terms:
2 + -18y + 10y2 = 10 + -10 + y + -1y

Combine like terms: 10 + -10 = 0
2 + -18y + 10y2 = 0 + y + -1y
2 + -18y + 10y2 = y + -1y

Combine like terms: y + -1y = 0
2 + -18y + 10y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -9y + 5y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -9y + 5y2)' equal to zero and attempt to solve:

Simplifying
1 + -9y + 5y2 = 0

Solving
1 + -9y + 5y2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
0.2 + -1.8y + y2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -1.8y + -0.2 + y2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -1.8y + y2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -1.8y + y2 = 0 + -0.2
-1.8y + y2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-1.8y + y2 = -0.2

The y term is -1.8y.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8y + 0.81 + y2 = -0.2 + 0.81

Reorder the terms:
0.81 + -1.8y + y2 = -0.2 + 0.81

Combine like terms: -0.2 + 0.81 = 0.61
0.81 + -1.8y + y2 = 0.61

Factor a perfect square on the left side:
(y + -0.9)(y + -0.9) = 0.61

Calculate the square root of the right side: 0.781024968

Break this problem into two subproblems by setting 
(y + -0.9) equal to 0.781024968 and -0.781024968.

Subproblem 1
y + -0.9 = 0.781024968

Simplifying
y + -0.9 = 0.781024968

Reorder the terms:
-0.9 + y = 0.781024968

Solving
-0.9 + y = 0.781024968

Solving for variable 'y'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + y = 0.781024968 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + y = 0.781024968 + 0.9
y = 0.781024968 + 0.9

Combine like terms: 0.781024968 + 0.9 = 1.681024968
y = 1.681024968

Simplifying
y = 1.681024968

Subproblem 2
y + -0.9 = -0.781024968

Simplifying
y + -0.9 = -0.781024968

Reorder the terms:
-0.9 + y = -0.781024968

Solving
-0.9 + y = -0.781024968

Solving for variable 'y'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + y = -0.781024968 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + y = -0.781024968 + 0.9
y = -0.781024968 + 0.9

Combine like terms: -0.781024968 + 0.9 = 0.118975032
y = 0.118975032

Simplifying
y = 0.118975032

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.681024968, 0.118975032}
Solution
y = {1.681024968, 0.118975032}