(4y-9)(2+y)=0

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Solution for (4y-9)(2+y)=0 equation: 


Simplifying
(4y + -9)(2 + y) = 0

Reorder the terms:
(-9 + 4y)(2 + y) = 0

Multiply (-9 + 4y) * (2 + y)
(-9(2 + y) + 4y * (2 + y)) = 0
((2 * -9 + y * -9) + 4y * (2 + y)) = 0
((-18 + -9y) + 4y * (2 + y)) = 0
(-18 + -9y + (2 * 4y + y * 4y)) = 0
(-18 + -9y + (8y + 4y2)) = 0

Combine like terms: -9y + 8y = -1y
(-18 + -1y + 4y2) = 0

Solving
-18 + -1y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-2 + -1y)(9 + -4y) = 0


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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1y = 0 + 2

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

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

Divide each side by '-1'.
y = -2

Simplifying
y = -2

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 = {-2, 2.25}

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