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

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


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

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

Reorder the terms:
((-5xz + 35x2) + 2z * (7x + -1z)) = 0
((-5xz + 35x2) + 2z * (7x + -1z)) = 0
(-5xz + 35x2 + (7x * 2z + -1z * 2z)) = 0
(-5xz + 35x2 + (14xz + -2z2)) = 0

Reorder the terms:
(-5xz + 14xz + 35x2 + -2z2) = 0

Combine like terms: -5xz + 14xz = 9xz
(9xz + 35x2 + -2z2) = 0

Solving
9xz + 35x2 + -2z2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(7x + -1z)' equal to zero and attempt to solve:

Simplifying
7x + -1z = 0

Solving
7x + -1z = 0

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

Add 'z' to each side of the equation.
7x + -1z + z = 0 + z

Combine like terms: -1z + z = 0
7x + 0 = 0 + z
7x = 0 + z
Remove the zero:
7x = z

Divide each side by '7'.
x = 0.1428571429z

Simplifying
x = 0.1428571429z

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

Simplifying
5x + 2z = 0

Solving
5x + 2z = 0

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

Add '-2z' to each side of the equation.
5x + 2z + -2z = 0 + -2z

Combine like terms: 2z + -2z = 0
5x + 0 = 0 + -2z
5x = 0 + -2z
Remove the zero:
5x = -2z

Divide each side by '5'.
x = -0.4z

Simplifying
x = -0.4z
Solution
x = {0.1428571429z, -0.4z}

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