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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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