(3z-4y)(9z+16y)=

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Solution for (3z-4y)(9z+16y)= equation: 


Simplifying
(3z + -4y)(9z + 16y) = 0

Reorder the terms:
(-4y + 3z)(9z + 16y) = 0

Reorder the terms:
(-4y + 3z)(16y + 9z) = 0

Multiply (-4y + 3z) * (16y + 9z)
(-4y * (16y + 9z) + 3z * (16y + 9z)) = 0
((16y * -4y + 9z * -4y) + 3z * (16y + 9z)) = 0

Reorder the terms:
((-36yz + -64y2) + 3z * (16y + 9z)) = 0
((-36yz + -64y2) + 3z * (16y + 9z)) = 0
(-36yz + -64y2 + (16y * 3z + 9z * 3z)) = 0
(-36yz + -64y2 + (48yz + 27z2)) = 0

Reorder the terms:
(-36yz + 48yz + -64y2 + 27z2) = 0

Combine like terms: -36yz + 48yz = 12yz
(12yz + -64y2 + 27z2) = 0

Solving
12yz + -64y2 + 27z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-16y + -9z)(4y + -3z) = 0


Subproblem 1
Set the factor '(-16y + -9z)' equal to zero and attempt to solve:

Simplifying
-16y + -9z = 0

Solving
-16y + -9z = 0

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

Add '9z' to each side of the equation.
-16y + -9z + 9z = 0 + 9z

Combine like terms: -9z + 9z = 0
-16y + 0 = 0 + 9z
-16y = 0 + 9z
Remove the zero:
-16y = 9z

Divide each side by '-16'.
y = -0.5625z

Simplifying
y = -0.5625z

Subproblem 2
Set the factor '(4y + -3z)' equal to zero and attempt to solve:

Simplifying
4y + -3z = 0

Solving
4y + -3z = 0

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

Add '3z' to each side of the equation.
4y + -3z + 3z = 0 + 3z

Combine like terms: -3z + 3z = 0
4y + 0 = 0 + 3z
4y = 0 + 3z
Remove the zero:
4y = 3z

Divide each side by '4'.
y = 0.75z

Simplifying
y = 0.75z
Solution
y = {-0.5625z, 0.75z}

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