(y-6)(y-5)=y+43

Solution for (y-6)(y-5)=y+43 equation:

Simplifying
(y + -6)(y + -5) = y + 43

Reorder the terms:
(-6 + y)(y + -5) = y + 43

Reorder the terms:
(-6 + y)(-5 + y) = y + 43

Multiply (-6 + y) * (-5 + y)
(-6(-5 + y) + y(-5 + y)) = y + 43
((-5 * -6 + y * -6) + y(-5 + y)) = y + 43
((30 + -6y) + y(-5 + y)) = y + 43
(30 + -6y + (-5 * y + y * y)) = y + 43
(30 + -6y + (-5y + y2)) = y + 43

Combine like terms: -6y + -5y = -11y
(30 + -11y + y2) = y + 43

Reorder the terms:
30 + -11y + y2 = 43 + y

Solving
30 + -11y + y2 = 43 + y

Solving for variable 'y'.

Reorder the terms:
30 + -43 + -11y + -1y + y2 = 43 + y + -43 + -1y

Combine like terms: 30 + -43 = -13
-13 + -11y + -1y + y2 = 43 + y + -43 + -1y

Combine like terms: -11y + -1y = -12y
-13 + -12y + y2 = 43 + y + -43 + -1y

Reorder the terms:
-13 + -12y + y2 = 43 + -43 + y + -1y

Combine like terms: 43 + -43 = 0
-13 + -12y + y2 = 0 + y + -1y
-13 + -12y + y2 = y + -1y

Combine like terms: y + -1y = 0
-13 + -12y + y2 = 0

Factor a trinomial.
(-1 + -1y)(13 + -1y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(13 + -1y)' equal to zero and attempt to solve:

Simplifying
13 + -1y = 0

Solving
13 + -1y = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1y = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1y = 0 + -13
-1y = 0 + -13

Combine like terms: 0 + -13 = -13
-1y = -13

Divide each side by '-1'.
y = 13

Simplifying
y = 13
Solution
y = {-1, 13}