(3y-2z)(7y+2z)=

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Solution for (3y-2z)(7y+2z)= equation: 


Simplifying
(3y + -2z)(7y + 2z) = 0

Multiply (3y + -2z) * (7y + 2z)
(3y * (7y + 2z) + -2z * (7y + 2z)) = 0
((7y * 3y + 2z * 3y) + -2z * (7y + 2z)) = 0

Reorder the terms:
((6yz + 21y2) + -2z * (7y + 2z)) = 0
((6yz + 21y2) + -2z * (7y + 2z)) = 0
(6yz + 21y2 + (7y * -2z + 2z * -2z)) = 0
(6yz + 21y2 + (-14yz + -4z2)) = 0

Reorder the terms:
(6yz + -14yz + 21y2 + -4z2) = 0

Combine like terms: 6yz + -14yz = -8yz
(-8yz + 21y2 + -4z2) = 0

Solving
-8yz + 21y2 + -4z2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3y + -2z)(7y + 2z) = 0


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

Simplifying
3y + -2z = 0

Solving
3y + -2z = 0

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

Add '2z' to each side of the equation.
3y + -2z + 2z = 0 + 2z

Combine like terms: -2z + 2z = 0
3y + 0 = 0 + 2z
3y = 0 + 2z
Remove the zero:
3y = 2z

Divide each side by '3'.
y = 0.6666666667z

Simplifying
y = 0.6666666667z

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

Simplifying
7y + 2z = 0

Solving
7y + 2z = 0

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

Add '-2z' to each side of the equation.
7y + 2z + -2z = 0 + -2z

Combine like terms: 2z + -2z = 0
7y + 0 = 0 + -2z
7y = 0 + -2z
Remove the zero:
7y = -2z

Divide each side by '7'.
y = -0.2857142857z

Simplifying
y = -0.2857142857z
Solution
y = {0.6666666667z, -0.2857142857z}

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