(y+3)(y-4)=0

Solution for (y+3)(y-4)=0 equation:

Simplifying
(y + 3)(y + -4) = 0

Reorder the terms:
(3 + y)(y + -4) = 0

Reorder the terms:
(3 + y)(-4 + y) = 0

Multiply (3 + y) * (-4 + y)
(3(-4 + y) + y(-4 + y)) = 0
((-4 * 3 + y * 3) + y(-4 + y)) = 0
((-12 + 3y) + y(-4 + y)) = 0
(-12 + 3y + (-4 * y + y * y)) = 0
(-12 + 3y + (-4y + y2)) = 0

Combine like terms: 3y + -4y = -1y
(-12 + -1y + y2) = 0

Solving
-12 + -1y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-3 + -1y)(4 + -1y) = 0

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

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 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 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3
Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {-3, 4}