(y-3)(y+4)=30

Solution for (y-3)(y+4)=30 equation:

Simplifying
(y + -3)(y + 4) = 30

Reorder the terms:
(-3 + y)(y + 4) = 30

Reorder the terms:
(-3 + y)(4 + y) = 30

Multiply (-3 + y) * (4 + y)
(-3(4 + y) + y(4 + y)) = 30
((4 * -3 + y * -3) + y(4 + y)) = 30
((-12 + -3y) + y(4 + y)) = 30
(-12 + -3y + (4 * y + y * y)) = 30
(-12 + -3y + (4y + y2)) = 30

Combine like terms: -3y + 4y = 1y
(-12 + 1y + y2) = 30

Solving
-12 + 1y + y2 = 30

Solving for variable 'y'.

Reorder the terms:
-12 + -30 + 1y + y2 = 30 + -30

Combine like terms: -12 + -30 = -42
-42 + 1y + y2 = 30 + -30

Combine like terms: 30 + -30 = 0
-42 + 1y + y2 = 0

Factor a trinomial.
(-7 + -1y)(6 + -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 '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {-7, 6}