7y^2-10y+11=y+17

Solution for 7y^2-10y+11=y+17 equation:

Simplifying
7y2 + -10y + 11 = y + 17

Reorder the terms:
11 + -10y + 7y2 = y + 17

Reorder the terms:
11 + -10y + 7y2 = 17 + y

Solving
11 + -10y + 7y2 = 17 + y

Solving for variable 'y'.

Reorder the terms:
11 + -17 + -10y + -1y + 7y2 = 17 + y + -17 + -1y

Combine like terms: 11 + -17 = -6
-6 + -10y + -1y + 7y2 = 17 + y + -17 + -1y

Combine like terms: -10y + -1y = -11y
-6 + -11y + 7y2 = 17 + y + -17 + -1y

Reorder the terms:
-6 + -11y + 7y2 = 17 + -17 + y + -1y

Combine like terms: 17 + -17 = 0
-6 + -11y + 7y2 = 0 + y + -1y
-6 + -11y + 7y2 = y + -1y

Combine like terms: y + -1y = 0
-6 + -11y + 7y2 = 0

Factor a trinomial.
(-3 + -7y)(2 + -1y) = 0

Subproblem 1
Set the factor '(-3 + -7y)' equal to zero and attempt to solve:

Simplifying
-3 + -7y = 0

Solving
-3 + -7y = 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 + -7y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7y = 0 + 3
-7y = 0 + 3

Combine like terms: 0 + 3 = 3
-7y = 3

Divide each side by '-7'.
y = -0.4285714286

Simplifying
y = -0.4285714286
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 = {-0.4285714286, 2}