(5y+4)(2y-1)=0

Solution for (5y+4)(2y-1)=0 equation:

Simplifying
(5y + 4)(2y + -1) = 0

Reorder the terms:
(4 + 5y)(2y + -1) = 0

Reorder the terms:
(4 + 5y)(-1 + 2y) = 0

Multiply (4 + 5y) * (-1 + 2y)
(4(-1 + 2y) + 5y * (-1 + 2y)) = 0
((-1 * 4 + 2y * 4) + 5y * (-1 + 2y)) = 0
((-4 + 8y) + 5y * (-1 + 2y)) = 0
(-4 + 8y + (-1 * 5y + 2y * 5y)) = 0
(-4 + 8y + (-5y + 10y2)) = 0

Combine like terms: 8y + -5y = 3y
(-4 + 3y + 10y2) = 0

Solving
-4 + 3y + 10y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-4 + -5y)(1 + -2y) = 0

Subproblem 1
Set the factor '(-4 + -5y)' equal to zero and attempt to solve:

Simplifying
-4 + -5y = 0

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

Combine like terms: -4 + 4 = 0
0 + -5y = 0 + 4
-5y = 0 + 4

Combine like terms: 0 + 4 = 4
-5y = 4

Divide each side by '-5'.
y = -0.8

Simplifying
y = -0.8
Subproblem 2
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
Solution
y = {-0.8, 0.5}