(3x-4z)(7x-2z)=

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Solution for (3x-4z)(7x-2z)= equation: 


Simplifying
(3x + -4z)(7x + -2z) = 0

Multiply (3x + -4z) * (7x + -2z)
(3x * (7x + -2z) + -4z * (7x + -2z)) = 0
((7x * 3x + -2z * 3x) + -4z * (7x + -2z)) = 0

Reorder the terms:
((-6xz + 21x2) + -4z * (7x + -2z)) = 0
((-6xz + 21x2) + -4z * (7x + -2z)) = 0
(-6xz + 21x2 + (7x * -4z + -2z * -4z)) = 0
(-6xz + 21x2 + (-28xz + 8z2)) = 0

Reorder the terms:
(-6xz + -28xz + 21x2 + 8z2) = 0

Combine like terms: -6xz + -28xz = -34xz
(-34xz + 21x2 + 8z2) = 0

Solving
-34xz + 21x2 + 8z2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + -4z)(7x + -2z) = 0


Subproblem 1
Set the factor '(3x + -4z)' equal to zero and attempt to solve:

Simplifying
3x + -4z = 0

Solving
3x + -4z = 0

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

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

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

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

Simplifying
x = 1.333333333z

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

Simplifying
7x + -2z = 0

Solving
7x + -2z = 0

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

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

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

Divide each side by '7'.
x = 0.2857142857z

Simplifying
x = 0.2857142857z
Solution
x = {1.333333333z, 0.2857142857z}

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