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

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


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

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

Multiply (-2 + 4y) * (9 + y)
(-2(9 + y) + 4y * (9 + y)) = 0
((9 * -2 + y * -2) + 4y * (9 + y)) = 0
((-18 + -2y) + 4y * (9 + y)) = 0
(-18 + -2y + (9 * 4y + y * 4y)) = 0
(-18 + -2y + (36y + 4y2)) = 0

Combine like terms: -2y + 36y = 34y
(-18 + 34y + 4y2) = 0

Solving
-18 + 34y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 17y + 2y2) = 0

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

Ignore the factor 2.

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

Simplifying
-9 + -1y = 0

Solving
-9 + -1y = 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 + -1y = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1y = 0 + 9
-1y = 0 + 9

Combine like terms: 0 + 9 = 9
-1y = 9

Divide each side by '-1'.
y = -9

Simplifying
y = -9

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 = {-9, 0.5}

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