(y-4)(y+1)=-6

Solution for (y-4)(y+1)=-6 equation:

Simplifying
(y + -4)(y + 1) = -6

Reorder the terms:
(-4 + y)(y + 1) = -6

Reorder the terms:
(-4 + y)(1 + y) = -6

Multiply (-4 + y) * (1 + y)
(-4(1 + y) + y(1 + y)) = -6
((1 * -4 + y * -4) + y(1 + y)) = -6
((-4 + -4y) + y(1 + y)) = -6
(-4 + -4y + (1 * y + y * y)) = -6
(-4 + -4y + (1y + y2)) = -6

Combine like terms: -4y + 1y = -3y
(-4 + -3y + y2) = -6

Solving
-4 + -3y + y2 = -6

Solving for variable 'y'.

Reorder the terms:
-4 + 6 + -3y + y2 = -6 + 6

Combine like terms: -4 + 6 = 2
2 + -3y + y2 = -6 + 6

Combine like terms: -6 + 6 = 0
2 + -3y + y2 = 0

Factor a trinomial.
(1 + -1y)(2 + -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 '(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 = {1, 2}