(3y-4z)(5y-6z)=

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Solution for (3y-4z)(5y-6z)= equation: 


Simplifying
(3y + -4z)(5y + -6z) = 0

Multiply (3y + -4z) * (5y + -6z)
(3y * (5y + -6z) + -4z * (5y + -6z)) = 0
((5y * 3y + -6z * 3y) + -4z * (5y + -6z)) = 0

Reorder the terms:
((-18yz + 15y2) + -4z * (5y + -6z)) = 0
((-18yz + 15y2) + -4z * (5y + -6z)) = 0
(-18yz + 15y2 + (5y * -4z + -6z * -4z)) = 0
(-18yz + 15y2 + (-20yz + 24z2)) = 0

Reorder the terms:
(-18yz + -20yz + 15y2 + 24z2) = 0

Combine like terms: -18yz + -20yz = -38yz
(-38yz + 15y2 + 24z2) = 0

Solving
-38yz + 15y2 + 24z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3y + -4z)(5y + -6z) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5y + -6z)' equal to zero and attempt to solve:

Simplifying
5y + -6z = 0

Solving
5y + -6z = 0

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

Add '6z' to each side of the equation.
5y + -6z + 6z = 0 + 6z

Combine like terms: -6z + 6z = 0
5y + 0 = 0 + 6z
5y = 0 + 6z
Remove the zero:
5y = 6z

Divide each side by '5'.
y = 1.2z

Simplifying
y = 1.2z
Solution
y = {1.333333333z, 1.2z}

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