(3y-5z)(8y+5z)=

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Solution for (3y-5z)(8y+5z)= equation: 


Simplifying
(3y + -5z)(8y + 5z) = 0

Multiply (3y + -5z) * (8y + 5z)
(3y * (8y + 5z) + -5z * (8y + 5z)) = 0
((8y * 3y + 5z * 3y) + -5z * (8y + 5z)) = 0

Reorder the terms:
((15yz + 24y2) + -5z * (8y + 5z)) = 0
((15yz + 24y2) + -5z * (8y + 5z)) = 0
(15yz + 24y2 + (8y * -5z + 5z * -5z)) = 0
(15yz + 24y2 + (-40yz + -25z2)) = 0

Reorder the terms:
(15yz + -40yz + 24y2 + -25z2) = 0

Combine like terms: 15yz + -40yz = -25yz
(-25yz + 24y2 + -25z2) = 0

Solving
-25yz + 24y2 + -25z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3y + -5z)(8y + 5z) = 0


Subproblem 1
Set the factor '(3y + -5z)' equal to zero and attempt to solve:

Simplifying
3y + -5z = 0

Solving
3y + -5z = 0

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

Add '5z' to each side of the equation.
3y + -5z + 5z = 0 + 5z

Combine like terms: -5z + 5z = 0
3y + 0 = 0 + 5z
3y = 0 + 5z
Remove the zero:
3y = 5z

Divide each side by '3'.
y = 1.666666667z

Simplifying
y = 1.666666667z

Subproblem 2
Set the factor '(8y + 5z)' equal to zero and attempt to solve:

Simplifying
8y + 5z = 0

Solving
8y + 5z = 0

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

Add '-5z' to each side of the equation.
8y + 5z + -5z = 0 + -5z

Combine like terms: 5z + -5z = 0
8y + 0 = 0 + -5z
8y = 0 + -5z
Remove the zero:
8y = -5z

Divide each side by '8'.
y = -0.625z

Simplifying
y = -0.625z
Solution
y = {1.666666667z, -0.625z}

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