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

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

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

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

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

Reorder the terms:
(5yz + -35yz + 7y2 + -25z2) = 0

Combine like terms: 5yz + -35yz = -30yz
(-30yz + 7y2 + -25z2) = 0

Solving
-30yz + 7y2 + -25z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(y + -5z)(7y + 5z) = 0

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

Simplifying
y + -5z = 0

Solving
y + -5z = 0

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

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

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

Simplifying
y = 5z
Subproblem 2
Set the factor '(7y + 5z)' equal to zero and attempt to solve:

Simplifying
7y + 5z = 0

Solving
7y + 5z = 0

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

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

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

Divide each side by '7'.
y = -0.7142857143z

Simplifying
y = -0.7142857143z
Solution
y = {5z, -0.7142857143z}