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

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

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

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

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

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

Combine like terms: -1y + 8y = 7y
(-4 + 7y + 2y2) = 5

Solving
-4 + 7y + 2y2 = 5

Solving for variable 'y'.

Reorder the terms:
-4 + -5 + 7y + 2y2 = 5 + -5

Combine like terms: -4 + -5 = -9
-9 + 7y + 2y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-9 + 7y + 2y2 = 0

Factor a trinomial.
(-9 + -2y)(1 + -1y) = 0

Subproblem 1
Set the factor '(-9 + -2y)' equal to zero and attempt to solve:

Simplifying
-9 + -2y = 0

Solving
-9 + -2y = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2y = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2y = 0 + 9
-2y = 0 + 9

Combine like terms: 0 + 9 = 9
-2y = 9

Divide each side by '-2'.
y = -4.5

Simplifying
y = -4.5
Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

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

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

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

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

Simplifying
y = 1
Solution
y = {-4.5, 1}