(y-4)(2y+1)=

Solution for (y-4)(2y+1)= equation:

Simplifying
(y + -4)(2y + 1) = 0

Reorder the terms:
(-4 + y)(2y + 1) = 0

Reorder the terms:
(-4 + y)(1 + 2y) = 0

Multiply (-4 + y) * (1 + 2y)
(-4(1 + 2y) + y(1 + 2y)) = 0
((1 * -4 + 2y * -4) + y(1 + 2y)) = 0
((-4 + -8y) + y(1 + 2y)) = 0
(-4 + -8y + (1 * y + 2y * y)) = 0
(-4 + -8y + (1y + 2y2)) = 0

Combine like terms: -8y + 1y = -7y
(-4 + -7y + 2y2) = 0

Solving
-4 + -7y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -2y)(4 + -1y) = 0

Subproblem 1
Set the factor '(-1 + -2y)' equal to zero and attempt to solve:

Simplifying
-1 + -2y = 0

Solving
-1 + -2y = 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 + -2y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2y = 0 + 1
-2y = 0 + 1

Combine like terms: 0 + 1 = 1
-2y = 1

Divide each side by '-2'.
y = -0.5

Simplifying
y = -0.5
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 = {-0.5, 4}