(3y-4z)(5y-7z)=

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Solution for (3y-4z)(5y-7z)= equation: 


Simplifying
(3y + -4z)(5y + -7z) = 0

Multiply (3y + -4z) * (5y + -7z)
(3y * (5y + -7z) + -4z * (5y + -7z)) = 0
((5y * 3y + -7z * 3y) + -4z * (5y + -7z)) = 0

Reorder the terms:
((-21yz + 15y2) + -4z * (5y + -7z)) = 0
((-21yz + 15y2) + -4z * (5y + -7z)) = 0
(-21yz + 15y2 + (5y * -4z + -7z * -4z)) = 0
(-21yz + 15y2 + (-20yz + 28z2)) = 0

Reorder the terms:
(-21yz + -20yz + 15y2 + 28z2) = 0

Combine like terms: -21yz + -20yz = -41yz
(-41yz + 15y2 + 28z2) = 0

Solving
-41yz + 15y2 + 28z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5y + -7z)(3y + -4z) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(3y + -4z)' equal to zero and attempt to solve:

Simplifying
3y + -4z = 0

Solving
3y + -4z = 0

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

Add '4z' to each side of the equation.
3y + -4z + 4z = 0 + 4z

Combine like terms: -4z + 4z = 0
3y + 0 = 0 + 4z
3y = 0 + 4z
Remove the zero:
3y = 4z

Divide each side by '3'.
y = 1.333333333z

Simplifying
y = 1.333333333z
Solution
y = {1.4z, 1.333333333z}

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