(Y-4)(Y+3)=

Solution for (Y-4)(Y+3)= equation:

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

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

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

Multiply (-4 + Y) * (3 + Y)
(-4(3 + Y) + Y(3 + Y)) = 0
((3 * -4 + Y * -4) + Y(3 + Y)) = 0
((-12 + -4Y) + Y(3 + Y)) = 0
(-12 + -4Y + (3 * Y + Y * Y)) = 0
(-12 + -4Y + (3Y + Y2)) = 0

Combine like terms: -4Y + 3Y = -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}