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

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


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

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

Reorder the terms:
((-9xz + 21x2) + 2z * (7x + -3z)) = 0
((-9xz + 21x2) + 2z * (7x + -3z)) = 0
(-9xz + 21x2 + (7x * 2z + -3z * 2z)) = 0
(-9xz + 21x2 + (14xz + -6z2)) = 0

Reorder the terms:
(-9xz + 14xz + 21x2 + -6z2) = 0

Combine like terms: -9xz + 14xz = 5xz
(5xz + 21x2 + -6z2) = 0

Solving
5xz + 21x2 + -6z2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(7x + -3z)' equal to zero and attempt to solve:

Simplifying
7x + -3z = 0

Solving
7x + -3z = 0

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

Add '3z' to each side of the equation.
7x + -3z + 3z = 0 + 3z

Combine like terms: -3z + 3z = 0
7x + 0 = 0 + 3z
7x = 0 + 3z
Remove the zero:
7x = 3z

Divide each side by '7'.
x = 0.4285714286z

Simplifying
x = 0.4285714286z

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 = {0.4285714286z, -0.6666666667z}

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