(4y-9)(1+y)=0

Solution for (4y-9)(1+y)=0 equation:

Simplifying
(4y + -9)(1 + y) = 0

Reorder the terms:
(-9 + 4y)(1 + y) = 0

Multiply (-9 + 4y) * (1 + y)
(-9(1 + y) + 4y * (1 + y)) = 0
((1 * -9 + y * -9) + 4y * (1 + y)) = 0
((-9 + -9y) + 4y * (1 + y)) = 0
(-9 + -9y + (1 * 4y + y * 4y)) = 0
(-9 + -9y + (4y + 4y2)) = 0

Combine like terms: -9y + 4y = -5y
(-9 + -5y + 4y2) = 0

Solving
-9 + -5y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -1y)(9 + -4y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -4y)' equal to zero and attempt to solve:

Simplifying
9 + -4y = 0

Solving
9 + -4y = 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 + -4y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4y = 0 + -9
-4y = 0 + -9

Combine like terms: 0 + -9 = -9
-4y = -9

Divide each side by '-4'.
y = 2.25

Simplifying
y = 2.25
Solution
y = {-1, 2.25}