(5y-4)(y+3)=0

Solution for (5y-4)(y+3)=0 equation:

Simplifying
(5y + -4)(y + 3) = 0

Reorder the terms:
(-4 + 5y)(y + 3) = 0

Reorder the terms:
(-4 + 5y)(3 + y) = 0

Multiply (-4 + 5y) * (3 + y)
(-4(3 + y) + 5y * (3 + y)) = 0
((3 * -4 + y * -4) + 5y * (3 + y)) = 0
((-12 + -4y) + 5y * (3 + y)) = 0
(-12 + -4y + (3 * 5y + y * 5y)) = 0
(-12 + -4y + (15y + 5y2)) = 0

Combine like terms: -4y + 15y = 11y
(-12 + 11y + 5y2) = 0

Solving
-12 + 11y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-3 + -1y)(4 + -5y) = 0

Subproblem 1
Set the factor '(-3 + -1y)' equal to zero and attempt to solve:

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3
Subproblem 2
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
Solution
y = {-3, 0.8}