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

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


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

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

Reorder the terms:
((-21xz + 6x2) + 2z * (2x + -7z)) = 0
((-21xz + 6x2) + 2z * (2x + -7z)) = 0
(-21xz + 6x2 + (2x * 2z + -7z * 2z)) = 0
(-21xz + 6x2 + (4xz + -14z2)) = 0

Reorder the terms:
(-21xz + 4xz + 6x2 + -14z2) = 0

Combine like terms: -21xz + 4xz = -17xz
(-17xz + 6x2 + -14z2) = 0

Solving
-17xz + 6x2 + -14z2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(2x + -7z)' equal to zero and attempt to solve:

Simplifying
2x + -7z = 0

Solving
2x + -7z = 0

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

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

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

Divide each side by '2'.
x = 3.5z

Simplifying
x = 3.5z

Subproblem 2
Set the factor '(3x + 2z)' equal to zero and attempt to solve:

Simplifying
3x + 2z = 0

Solving
3x + 2z = 0

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

Add '-2z' to each side of the equation.
3x + 2z + -2z = 0 + -2z

Combine like terms: 2z + -2z = 0
3x + 0 = 0 + -2z
3x = 0 + -2z
Remove the zero:
3x = -2z

Divide each side by '3'.
x = -0.6666666667z

Simplifying
x = -0.6666666667z
Solution
x = {3.5z, -0.6666666667z}

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