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

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


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

Reorder the terms:
2(3x + -2y)(4 + z) = 0

Multiply (3x + -2y) * (4 + z)
2(3x * (4 + z) + -2y * (4 + z)) = 0
2((4 * 3x + z * 3x) + -2y * (4 + z)) = 0
2((12x + 3xz) + -2y * (4 + z)) = 0
2(12x + 3xz + (4 * -2y + z * -2y)) = 0
2(12x + 3xz + (-8y + -2yz)) = 0
2(12x + 3xz + -8y + -2yz) = 0
(12x * 2 + 3xz * 2 + -8y * 2 + -2yz * 2) = 0
(24x + 6xz + -16y + -4yz) = 0

Solving
24x + 6xz + -16y + -4yz = 0

Solving for variable 'x'.

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

Add '16y' to each side of the equation.
24x + 6xz + -16y + 16y + -4yz = 0 + 16y

Combine like terms: -16y + 16y = 0
24x + 6xz + 0 + -4yz = 0 + 16y
24x + 6xz + -4yz = 0 + 16y
Remove the zero:
24x + 6xz + -4yz = 16y

Add '4yz' to each side of the equation.
24x + 6xz + -4yz + 4yz = 16y + 4yz

Combine like terms: -4yz + 4yz = 0
24x + 6xz + 0 = 16y + 4yz
24x + 6xz = 16y + 4yz

Reorder the terms:
24x + 6xz + -16y + -4yz = 16y + -16y + 4yz + -4yz

Combine like terms: 16y + -16y = 0
24x + 6xz + -16y + -4yz = 0 + 4yz + -4yz
24x + 6xz + -16y + -4yz = 4yz + -4yz

Combine like terms: 4yz + -4yz = 0
24x + 6xz + -16y + -4yz = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12x + 3xz + -8y + -2yz) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(12x + 3xz + -8y + -2yz)' equal to zero and attempt to solve: Simplifying 12x + 3xz + -8y + -2yz = 0 Solving 12x + 3xz + -8y + -2yz = 0 Move all terms containing x to the left, all other terms to the right. Add '8y' to each side of the equation. 12x + 3xz + -8y + 8y + -2yz = 0 + 8y Combine like terms: -8y + 8y = 0 12x + 3xz + 0 + -2yz = 0 + 8y 12x + 3xz + -2yz = 0 + 8y Remove the zero: 12x + 3xz + -2yz = 8y Add '2yz' to each side of the equation. 12x + 3xz + -2yz + 2yz = 8y + 2yz Combine like terms: -2yz + 2yz = 0 12x + 3xz + 0 = 8y + 2yz 12x + 3xz = 8y + 2yz The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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