(3y-5z)(5y-7z)=

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Solution for (3y-5z)(5y-7z)= equation: 


Simplifying
(3y + -5z)(5y + -7z) = 0

Multiply (3y + -5z) * (5y + -7z)
(3y * (5y + -7z) + -5z * (5y + -7z)) = 0
((5y * 3y + -7z * 3y) + -5z * (5y + -7z)) = 0

Reorder the terms:
((-21yz + 15y2) + -5z * (5y + -7z)) = 0
((-21yz + 15y2) + -5z * (5y + -7z)) = 0
(-21yz + 15y2 + (5y * -5z + -7z * -5z)) = 0
(-21yz + 15y2 + (-25yz + 35z2)) = 0

Reorder the terms:
(-21yz + -25yz + 15y2 + 35z2) = 0

Combine like terms: -21yz + -25yz = -46yz
(-46yz + 15y2 + 35z2) = 0

Solving
-46yz + 15y2 + 35z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3y + -5z)(5y + -7z) = 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 '(5y + -7z)' equal to zero and attempt to solve:

Simplifying
5y + -7z = 0

Solving
5y + -7z = 0

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

Add '7z' to each side of the equation.
5y + -7z + 7z = 0 + 7z

Combine like terms: -7z + 7z = 0
5y + 0 = 0 + 7z
5y = 0 + 7z
Remove the zero:
5y = 7z

Divide each side by '5'.
y = 1.4z

Simplifying
y = 1.4z
Solution
y = {1.666666667z, 1.4z}

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