(3x-5z)(2x+4z)=0

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Solution for (3x-5z)(2x+4z)=0 equation: 


Simplifying
(3x + -5z)(2x + 4z) = 0

Multiply (3x + -5z) * (2x + 4z)
(3x * (2x + 4z) + -5z * (2x + 4z)) = 0
((2x * 3x + 4z * 3x) + -5z * (2x + 4z)) = 0

Reorder the terms:
((12xz + 6x2) + -5z * (2x + 4z)) = 0
((12xz + 6x2) + -5z * (2x + 4z)) = 0
(12xz + 6x2 + (2x * -5z + 4z * -5z)) = 0
(12xz + 6x2 + (-10xz + -20z2)) = 0

Reorder the terms:
(12xz + -10xz + 6x2 + -20z2) = 0

Combine like terms: 12xz + -10xz = 2xz
(2xz + 6x2 + -20z2) = 0

Solving
2xz + 6x2 + -20z2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(xz + 3x2 + -10z2) = 0

Factor a trinomial.
2((3x + -5z)(x + 2z)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3x + -5z)' equal to zero and attempt to solve:

Simplifying
3x + -5z = 0

Solving
3x + -5z = 0

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

Add '5z' to each side of the equation.
3x + -5z + 5z = 0 + 5z

Combine like terms: -5z + 5z = 0
3x + 0 = 0 + 5z
3x = 0 + 5z
Remove the zero:
3x = 5z

Divide each side by '3'.
x = 1.666666667z

Simplifying
x = 1.666666667z

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

Simplifying
x + 2z = 0

Solving
x + 2z = 0

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

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

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

Simplifying
x = -2z
Solution
x = {1.666666667z, -2z}

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