(3x-2z)(4x-7z)=

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Solution for (3x-2z)(4x-7z)= equation: 


Simplifying
(3x + -2z)(4x + -7z) = 0

Multiply (3x + -2z) * (4x + -7z)
(3x * (4x + -7z) + -2z * (4x + -7z)) = 0
((4x * 3x + -7z * 3x) + -2z * (4x + -7z)) = 0

Reorder the terms:
((-21xz + 12x2) + -2z * (4x + -7z)) = 0
((-21xz + 12x2) + -2z * (4x + -7z)) = 0
(-21xz + 12x2 + (4x * -2z + -7z * -2z)) = 0
(-21xz + 12x2 + (-8xz + 14z2)) = 0

Reorder the terms:
(-21xz + -8xz + 12x2 + 14z2) = 0

Combine like terms: -21xz + -8xz = -29xz
(-29xz + 12x2 + 14z2) = 0

Solving
-29xz + 12x2 + 14z2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4x + -7z)(3x + -2z) = 0


Subproblem 1
Set the factor '(4x + -7z)' equal to zero and attempt to solve:

Simplifying
4x + -7z = 0

Solving
4x + -7z = 0

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

Add '7z' to each side of the equation.
4x + -7z + 7z = 0 + 7z

Combine like terms: -7z + 7z = 0
4x + 0 = 0 + 7z
4x = 0 + 7z
Remove the zero:
4x = 7z

Divide each side by '4'.
x = 1.75z

Simplifying
x = 1.75z

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 = {1.75z, 0.6666666667z}

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