(4x-3z)(8x-z)=0

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Solution for (4x-3z)(8x-z)=0 equation: 


Simplifying
(4x + -3z)(8x + -1z) = 0

Multiply (4x + -3z) * (8x + -1z)
(4x * (8x + -1z) + -3z * (8x + -1z)) = 0
((8x * 4x + -1z * 4x) + -3z * (8x + -1z)) = 0

Reorder the terms:
((-4xz + 32x2) + -3z * (8x + -1z)) = 0
((-4xz + 32x2) + -3z * (8x + -1z)) = 0
(-4xz + 32x2 + (8x * -3z + -1z * -3z)) = 0
(-4xz + 32x2 + (-24xz + 3z2)) = 0

Reorder the terms:
(-4xz + -24xz + 32x2 + 3z2) = 0

Combine like terms: -4xz + -24xz = -28xz
(-28xz + 32x2 + 3z2) = 0

Solving
-28xz + 32x2 + 3z2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4x + -3z)(8x + -1z) = 0


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

Simplifying
4x + -3z = 0

Solving
4x + -3z = 0

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

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

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

Divide each side by '4'.
x = 0.75z

Simplifying
x = 0.75z

Subproblem 2
Set the factor '(8x + -1z)' equal to zero and attempt to solve:

Simplifying
8x + -1z = 0

Solving
8x + -1z = 0

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

Add 'z' to each side of the equation.
8x + -1z + z = 0 + z

Combine like terms: -1z + z = 0
8x + 0 = 0 + z
8x = 0 + z
Remove the zero:
8x = z

Divide each side by '8'.
x = 0.125z

Simplifying
x = 0.125z
Solution
x = {0.75z, 0.125z}

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