(y-7)(8y+17)=0

Solution for (y-7)(8y+17)=0 equation:

Simplifying
(y + -7)(8y + 17) = 0

Reorder the terms:
(-7 + y)(8y + 17) = 0

Reorder the terms:
(-7 + y)(17 + 8y) = 0

Multiply (-7 + y) * (17 + 8y)
(-7(17 + 8y) + y(17 + 8y)) = 0
((17 * -7 + 8y * -7) + y(17 + 8y)) = 0
((-119 + -56y) + y(17 + 8y)) = 0
(-119 + -56y + (17 * y + 8y * y)) = 0
(-119 + -56y + (17y + 8y2)) = 0

Combine like terms: -56y + 17y = -39y
(-119 + -39y + 8y2) = 0

Solving
-119 + -39y + 8y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-17 + -8y)(7 + -1y) = 0

Subproblem 1
Set the factor '(-17 + -8y)' equal to zero and attempt to solve:

Simplifying
-17 + -8y = 0

Solving
-17 + -8y = 0

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

Add '17' to each side of the equation.
-17 + 17 + -8y = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -8y = 0 + 17
-8y = 0 + 17

Combine like terms: 0 + 17 = 17
-8y = 17

Divide each side by '-8'.
y = -2.125

Simplifying
y = -2.125
Subproblem 2
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
Solution
y = {-2.125, 7}