2y^2+y-1=y^2-5y+6

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Solution for 2y^2+y-1=y^2-5y+6 equation: 


Simplifying
2y2 + y + -1 = y2 + -5y + 6

Reorder the terms:
-1 + y + 2y2 = y2 + -5y + 6

Reorder the terms:
-1 + y + 2y2 = 6 + -5y + y2

Solving
-1 + y + 2y2 = 6 + -5y + y2

Solving for variable 'y'.

Reorder the terms:
-1 + -6 + y + 5y + 2y2 + -1y2 = 6 + -5y + y2 + -6 + 5y + -1y2

Combine like terms: -1 + -6 = -7
-7 + y + 5y + 2y2 + -1y2 = 6 + -5y + y2 + -6 + 5y + -1y2

Combine like terms: y + 5y = 6y
-7 + 6y + 2y2 + -1y2 = 6 + -5y + y2 + -6 + 5y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-7 + 6y + 1y2 = 6 + -5y + y2 + -6 + 5y + -1y2

Reorder the terms:
-7 + 6y + 1y2 = 6 + -6 + -5y + 5y + y2 + -1y2

Combine like terms: 6 + -6 = 0
-7 + 6y + 1y2 = 0 + -5y + 5y + y2 + -1y2
-7 + 6y + 1y2 = -5y + 5y + y2 + -1y2

Combine like terms: -5y + 5y = 0
-7 + 6y + 1y2 = 0 + y2 + -1y2
-7 + 6y + 1y2 = y2 + -1y2

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

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


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

Simplifying
-7 + -1y = 0

Solving
-7 + -1y = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1y = 0 + 7
-1y = 0 + 7

Combine like terms: 0 + 7 = 7
-1y = 7

Divide each side by '-1'.
y = -7

Simplifying
y = -7

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

Simplifying
1 + -1y = 0

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

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

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

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

Simplifying
y = 1
Solution
y = {-7, 1}

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