y^2-4yz-21z^2=0

Solution for y^2-4yz-21z^2=0 equation:

Simplifying
y2 + -4yz + -21z2 = 0

Reorder the terms:
-4yz + y2 + -21z2 = 0

Solving
-4yz + y2 + -21z2 = 0

Solving for variable 'y'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(y + 3z)' equal to zero and attempt to solve:

Simplifying
y + 3z = 0

Solving
y + 3z = 0

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

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

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

Simplifying
y = -3z
Solution
y = {7z, -3z}