(8y+27)(8y+21)=0

Solution for (8y+27)(8y+21)=0 equation:

Simplifying
(8y + 27)(8y + 21) = 0

Reorder the terms:
(27 + 8y)(8y + 21) = 0

Reorder the terms:
(27 + 8y)(21 + 8y) = 0

Multiply (27 + 8y) * (21 + 8y)
(27(21 + 8y) + 8y * (21 + 8y)) = 0
((21 * 27 + 8y * 27) + 8y * (21 + 8y)) = 0
((567 + 216y) + 8y * (21 + 8y)) = 0
(567 + 216y + (21 * 8y + 8y * 8y)) = 0
(567 + 216y + (168y + 64y2)) = 0

Combine like terms: 216y + 168y = 384y
(567 + 384y + 64y2) = 0

Solving
567 + 384y + 64y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(27 + 8y)(21 + 8y) = 0

Subproblem 1
Set the factor '(27 + 8y)' equal to zero and attempt to solve:

Simplifying
27 + 8y = 0

Solving
27 + 8y = 0

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

Add '-27' to each side of the equation.
27 + -27 + 8y = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 8y = 0 + -27
8y = 0 + -27

Combine like terms: 0 + -27 = -27
8y = -27

Divide each side by '8'.
y = -3.375

Simplifying
y = -3.375
Subproblem 2
Set the factor '(21 + 8y)' equal to zero and attempt to solve:

Simplifying
21 + 8y = 0

Solving
21 + 8y = 0

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

Add '-21' to each side of the equation.
21 + -21 + 8y = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 8y = 0 + -21
8y = 0 + -21

Combine like terms: 0 + -21 = -21
8y = -21

Divide each side by '8'.
y = -2.625

Simplifying
y = -2.625
Solution
y = {-3.375, -2.625}