(3y+z)(3y-8z)=

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Solution for (3y+z)(3y-8z)= equation: 


Simplifying
(3y + z)(3y + -8z) = 0

Multiply (3y + z) * (3y + -8z)
(3y * (3y + -8z) + z(3y + -8z)) = 0
((3y * 3y + -8z * 3y) + z(3y + -8z)) = 0

Reorder the terms:
((-24yz + 9y2) + z(3y + -8z)) = 0
((-24yz + 9y2) + z(3y + -8z)) = 0
(-24yz + 9y2 + (3y * z + -8z * z)) = 0
(-24yz + 9y2 + (3yz + -8z2)) = 0

Reorder the terms:
(-24yz + 3yz + 9y2 + -8z2) = 0

Combine like terms: -24yz + 3yz = -21yz
(-21yz + 9y2 + -8z2) = 0

Solving
-21yz + 9y2 + -8z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3y + -8z)(3y + z) = 0


Subproblem 1
Set the factor '(3y + -8z)' equal to zero and attempt to solve:

Simplifying
3y + -8z = 0

Solving
3y + -8z = 0

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

Add '8z' to each side of the equation.
3y + -8z + 8z = 0 + 8z

Combine like terms: -8z + 8z = 0
3y + 0 = 0 + 8z
3y = 0 + 8z
Remove the zero:
3y = 8z

Divide each side by '3'.
y = 2.666666667z

Simplifying
y = 2.666666667z

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

Simplifying
3y + z = 0

Solving
3y + z = 0

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

Add '-1z' to each side of the equation.
3y + z + -1z = 0 + -1z

Combine like terms: z + -1z = 0
3y + 0 = 0 + -1z
3y = 0 + -1z
Remove the zero:
3y = -1z

Divide each side by '3'.
y = -0.3333333333z

Simplifying
y = -0.3333333333z
Solution
y = {2.666666667z, -0.3333333333z}

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