(4y+1)(y-6)=0

Solution for (4y+1)(y-6)=0 equation:

Simplifying
(4y + 1)(y + -6) = 0

Reorder the terms:
(1 + 4y)(y + -6) = 0

Reorder the terms:
(1 + 4y)(-6 + y) = 0

Multiply (1 + 4y) * (-6 + y)
(1(-6 + y) + 4y * (-6 + y)) = 0
((-6 * 1 + y * 1) + 4y * (-6 + y)) = 0
((-6 + 1y) + 4y * (-6 + y)) = 0
(-6 + 1y + (-6 * 4y + y * 4y)) = 0
(-6 + 1y + (-24y + 4y2)) = 0

Combine like terms: 1y + -24y = -23y
(-6 + -23y + 4y2) = 0

Solving
-6 + -23y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -4y)(6 + -1y) = 0

Subproblem 1
Set the factor '(-1 + -4y)' equal to zero and attempt to solve:

Simplifying
-1 + -4y = 0

Solving
-1 + -4y = 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 + -4y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4y = 0 + 1
-4y = 0 + 1

Combine like terms: 0 + 1 = 1
-4y = 1

Divide each side by '-4'.
y = -0.25

Simplifying
y = -0.25
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 = {-0.25, 6}