(y-3)(y+7)=0

Solution for (y-3)(y+7)=0 equation:

Simplifying
(y + -3)(y + 7) = 0

Reorder the terms:
(-3 + y)(y + 7) = 0

Reorder the terms:
(-3 + y)(7 + y) = 0

Multiply (-3 + y) * (7 + y)
(-3(7 + y) + y(7 + y)) = 0
((7 * -3 + y * -3) + y(7 + y)) = 0
((-21 + -3y) + y(7 + y)) = 0
(-21 + -3y + (7 * y + y * y)) = 0
(-21 + -3y + (7y + y2)) = 0

Combine like terms: -3y + 7y = 4y
(-21 + 4y + y2) = 0

Solving
-21 + 4y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-7 + -1y)(3 + -1y) = 0

Subproblem 1
Set the factor '(-7 + -1y)' equal to zero and attempt to solve:

Simplifying
-7 + -1y = 0

Solving
-7 + -1y = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1y = 0 + 7
-1y = 0 + 7

Combine like terms: 0 + 7 = 7
-1y = 7

Divide each side by '-1'.
y = -7

Simplifying
y = -7
Subproblem 2
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
Solution
y = {-7, 3}