(y-4)(5y+1)=0

Solution for (y-4)(5y+1)=0 equation:

Simplifying
(y + -4)(5y + 1) = 0

Reorder the terms:
(-4 + y)(5y + 1) = 0

Reorder the terms:
(-4 + y)(1 + 5y) = 0

Multiply (-4 + y) * (1 + 5y)
(-4(1 + 5y) + y(1 + 5y)) = 0
((1 * -4 + 5y * -4) + y(1 + 5y)) = 0
((-4 + -20y) + y(1 + 5y)) = 0
(-4 + -20y + (1 * y + 5y * y)) = 0
(-4 + -20y + (1y + 5y2)) = 0

Combine like terms: -20y + 1y = -19y
(-4 + -19y + 5y2) = 0

Solving
-4 + -19y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -5y)(4 + -1y) = 0

Subproblem 1
Set the factor '(-1 + -5y)' equal to zero and attempt to solve:

Simplifying
-1 + -5y = 0

Solving
-1 + -5y = 0

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

Add '1' to each side of the equation.
-1 + 1 + -5y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5y = 0 + 1
-5y = 0 + 1

Combine like terms: 0 + 1 = 1
-5y = 1

Divide each side by '-5'.
y = -0.2

Simplifying
y = -0.2
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 = {-0.2, 4}