(5x-z)(7x-2z)=

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Solution for (5x-z)(7x-2z)= equation: 


Simplifying
(5x + -1z)(7x + -2z) = 0

Multiply (5x + -1z) * (7x + -2z)
(5x * (7x + -2z) + -1z * (7x + -2z)) = 0
((7x * 5x + -2z * 5x) + -1z * (7x + -2z)) = 0

Reorder the terms:
((-10xz + 35x2) + -1z * (7x + -2z)) = 0
((-10xz + 35x2) + -1z * (7x + -2z)) = 0
(-10xz + 35x2 + (7x * -1z + -2z * -1z)) = 0
(-10xz + 35x2 + (-7xz + 2z2)) = 0

Reorder the terms:
(-10xz + -7xz + 35x2 + 2z2) = 0

Combine like terms: -10xz + -7xz = -17xz
(-17xz + 35x2 + 2z2) = 0

Solving
-17xz + 35x2 + 2z2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7x + -2z)(5x + -1z) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5x + -1z)' equal to zero and attempt to solve:

Simplifying
5x + -1z = 0

Solving
5x + -1z = 0

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

Add 'z' to each side of the equation.
5x + -1z + z = 0 + z

Combine like terms: -1z + z = 0
5x + 0 = 0 + z
5x = 0 + z
Remove the zero:
5x = z

Divide each side by '5'.
x = 0.2z

Simplifying
x = 0.2z
Solution
x = {0.2857142857z, 0.2z}

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