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Simplifying (8x + 4)(5z + 10) = 0 Reorder the terms: (4 + 8x)(5z + 10) = 0 Reorder the terms: (4 + 8x)(10 + 5z) = 0 Multiply (4 + 8x) * (10 + 5z) (4(10 + 5z) + 8x * (10 + 5z)) = 0 ((10 * 4 + 5z * 4) + 8x * (10 + 5z)) = 0 ((40 + 20z) + 8x * (10 + 5z)) = 0 (40 + 20z + (10 * 8x + 5z * 8x)) = 0 (40 + 20z + (80x + 40xz)) = 0 Reorder the terms: (40 + 80x + 40xz + 20z) = 0 (40 + 80x + 40xz + 20z) = 0 Solving 40 + 80x + 40xz + 20z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + 80x + 40xz + -40 + 20z = 0 + -40 Reorder the terms: 40 + -40 + 80x + 40xz + 20z = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 80x + 40xz + 20z = 0 + -40 80x + 40xz + 20z = 0 + -40 Combine like terms: 0 + -40 = -40 80x + 40xz + 20z = -40 Add '-20z' to each side of the equation. 80x + 40xz + 20z + -20z = -40 + -20z Combine like terms: 20z + -20z = 0 80x + 40xz + 0 = -40 + -20z 80x + 40xz = -40 + -20z Reorder the terms: 40 + 80x + 40xz + 20z = -40 + -20z + 40 + 20z Reorder the terms: 40 + 80x + 40xz + 20z = -40 + 40 + -20z + 20z Combine like terms: -40 + 40 = 0 40 + 80x + 40xz + 20z = 0 + -20z + 20z 40 + 80x + 40xz + 20z = -20z + 20z Combine like terms: -20z + 20z = 0 40 + 80x + 40xz + 20z = 0 Factor out the Greatest Common Factor (GCF), '20'. 20(2 + 4x + 2xz + z) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(2 + 4x + 2xz + z)' equal to zero and attempt to solve: Simplifying 2 + 4x + 2xz + z = 0 Solving 2 + 4x + 2xz + z = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + 4x + 2xz + -2 + z = 0 + -2 Reorder the terms: 2 + -2 + 4x + 2xz + z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 4x + 2xz + z = 0 + -2 4x + 2xz + z = 0 + -2 Combine like terms: 0 + -2 = -2 4x + 2xz + z = -2 Add '-1z' to each side of the equation. 4x + 2xz + z + -1z = -2 + -1z Combine like terms: z + -1z = 0 4x + 2xz + 0 = -2 + -1z 4x + 2xz = -2 + -1z 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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