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

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

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

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

Reorder the terms:
((3yz + 3y2) + -5z * (y + z)) = 0
((3yz + 3y2) + -5z * (y + z)) = 0
(3yz + 3y2 + (y * -5z + z * -5z)) = 0
(3yz + 3y2 + (-5yz + -5z2)) = 0

Reorder the terms:
(3yz + -5yz + 3y2 + -5z2) = 0

Combine like terms: 3yz + -5yz = -2yz
(-2yz + 3y2 + -5z2) = 0

Solving
-2yz + 3y2 + -5z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3y + -5z)(y + z) = 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 '(y + z)' equal to zero and attempt to solve:

Simplifying
y + z = 0

Solving
y + z = 0

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

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

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

Simplifying
y = -1z
Solution
y = {1.666666667z, -1z}