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Simplifying 0 = 4z + 8z * 8z Reorder the terms for easier multiplication: 0 = 4z + 8 * 8z * z Multiply 8 * 8 0 = 4z + 64z * z Multiply z * z 0 = 4z + 64z2 Solving 0 = 4z + 64z2 Solving for variable 'z'. Remove the zero: -4z + -64z2 = 4z + 64z2 + -4z + -64z2 Reorder the terms: -4z + -64z2 = 4z + -4z + 64z2 + -64z2 Combine like terms: 4z + -4z = 0 -4z + -64z2 = 0 + 64z2 + -64z2 -4z + -64z2 = 64z2 + -64z2 Combine like terms: 64z2 + -64z2 = 0 -4z + -64z2 = 0 Factor out the Greatest Common Factor (GCF), '-4z'. -4z(1 + 16z) = 0 Ignore the factor -4.Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(1 + 16z)' equal to zero and attempt to solve: Simplifying 1 + 16z = 0 Solving 1 + 16z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 16z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 16z = 0 + -1 16z = 0 + -1 Combine like terms: 0 + -1 = -1 16z = -1 Divide each side by '16'. z = -0.0625 Simplifying z = -0.0625Solution
z = {0, -0.0625}
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