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

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

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

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

Reorder the terms:
((21yz + 3y2) + -4z * (y + 7z)) = 0
((21yz + 3y2) + -4z * (y + 7z)) = 0
(21yz + 3y2 + (y * -4z + 7z * -4z)) = 0
(21yz + 3y2 + (-4yz + -28z2)) = 0

Reorder the terms:
(21yz + -4yz + 3y2 + -28z2) = 0

Combine like terms: 21yz + -4yz = 17yz
(17yz + 3y2 + -28z2) = 0

Solving
17yz + 3y2 + -28z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3y + -4z)(y + 7z) = 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 '(y + 7z)' equal to zero and attempt to solve:

Simplifying
y + 7z = 0

Solving
y + 7z = 0

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

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

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

Simplifying
y = -7z
Solution
y = {1.333333333z, -7z}