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Simplifying 4z(3z + 2) + -4z(4z + 7) = 0 Reorder the terms: 4z(2 + 3z) + -4z(4z + 7) = 0 (2 * 4z + 3z * 4z) + -4z(4z + 7) = 0 (8z + 12z2) + -4z(4z + 7) = 0 Reorder the terms: 8z + 12z2 + -4z(7 + 4z) = 0 8z + 12z2 + (7 * -4z + 4z * -4z) = 0 8z + 12z2 + (-28z + -16z2) = 0 Reorder the terms: 8z + -28z + 12z2 + -16z2 = 0 Combine like terms: 8z + -28z = -20z -20z + 12z2 + -16z2 = 0 Combine like terms: 12z2 + -16z2 = -4z2 -20z + -4z2 = 0 Solving -20z + -4z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '-4z'. -4z(5 + z) = 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 '(5 + z)' equal to zero and attempt to solve: Simplifying 5 + z = 0 Solving 5 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + z = 0 + -5 z = 0 + -5 Combine like terms: 0 + -5 = -5 z = -5 Simplifying z = -5Solution
z = {0, -5}
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