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Simplifying (4 + z)(4z + -1) = 0 Reorder the terms: (4 + z)(-1 + 4z) = 0 Multiply (4 + z) * (-1 + 4z) (4(-1 + 4z) + z(-1 + 4z)) = 0 ((-1 * 4 + 4z * 4) + z(-1 + 4z)) = 0 ((-4 + 16z) + z(-1 + 4z)) = 0 (-4 + 16z + (-1 * z + 4z * z)) = 0 (-4 + 16z + (-1z + 4z2)) = 0 Combine like terms: 16z + -1z = 15z (-4 + 15z + 4z2) = 0 Solving -4 + 15z + 4z2 = 0 Solving for variable 'z'. Factor a trinomial. (-4 + -1z)(1 + -4z) = 0Subproblem 1
Set the factor '(-4 + -1z)' equal to zero and attempt to solve: Simplifying -4 + -1z = 0 Solving -4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1z = 0 + 4 -1z = 0 + 4 Combine like terms: 0 + 4 = 4 -1z = 4 Divide each side by '-1'. z = -4 Simplifying z = -4Subproblem 2
Set the factor '(1 + -4z)' equal to zero and attempt to solve: Simplifying 1 + -4z = 0 Solving 1 + -4z = 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 + -4z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4z = 0 + -1 -4z = 0 + -1 Combine like terms: 0 + -1 = -1 -4z = -1 Divide each side by '-4'. z = 0.25 Simplifying z = 0.25Solution
z = {-4, 0.25}
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