2y^2-9y+43=y^2-14y+49

Solution for 2y^2-9y+43=y^2-14y+49 equation:

Simplifying
2y2 + -9y + 43 = y2 + -14y + 49

Reorder the terms:
43 + -9y + 2y2 = y2 + -14y + 49

Reorder the terms:
43 + -9y + 2y2 = 49 + -14y + y2

Solving
43 + -9y + 2y2 = 49 + -14y + y2

Solving for variable 'y'.

Reorder the terms:
43 + -49 + -9y + 14y + 2y2 + -1y2 = 49 + -14y + y2 + -49 + 14y + -1y2

Combine like terms: 43 + -49 = -6
-6 + -9y + 14y + 2y2 + -1y2 = 49 + -14y + y2 + -49 + 14y + -1y2

Combine like terms: -9y + 14y = 5y
-6 + 5y + 2y2 + -1y2 = 49 + -14y + y2 + -49 + 14y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-6 + 5y + 1y2 = 49 + -14y + y2 + -49 + 14y + -1y2

Reorder the terms:
-6 + 5y + 1y2 = 49 + -49 + -14y + 14y + y2 + -1y2

Combine like terms: 49 + -49 = 0
-6 + 5y + 1y2 = 0 + -14y + 14y + y2 + -1y2
-6 + 5y + 1y2 = -14y + 14y + y2 + -1y2

Combine like terms: -14y + 14y = 0
-6 + 5y + 1y2 = 0 + y2 + -1y2
-6 + 5y + 1y2 = y2 + -1y2

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

Factor a trinomial.
(-6 + -1y)(1 + -1y) = 0

Subproblem 1
Set the factor '(-6 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1y = 0 + 6

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

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

Divide each side by '-1'.
y = -6

Simplifying
y = -6
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 = {-6, 1}