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Simplifying (z2 + -16)(z2 + -49) = 0 Reorder the terms: (-16 + z2)(z2 + -49) = 0 Reorder the terms: (-16 + z2)(-49 + z2) = 0 Multiply (-16 + z2) * (-49 + z2) (-16(-49 + z2) + z2(-49 + z2)) = 0 ((-49 * -16 + z2 * -16) + z2(-49 + z2)) = 0 ((784 + -16z2) + z2(-49 + z2)) = 0 (784 + -16z2 + (-49 * z2 + z2 * z2)) = 0 (784 + -16z2 + (-49z2 + z4)) = 0 Combine like terms: -16z2 + -49z2 = -65z2 (784 + -65z2 + z4) = 0 Solving 784 + -65z2 + z4 = 0 Solving for variable 'z'. Factor a trinomial. (16 + -1z2)(49 + -1z2) = 0 Factor a difference between two squares. ((4 + z)(4 + -1z))(49 + -1z2) = 0 Factor a difference between two squares. ((7 + z)(7 + -1z))(4 + z)(4 + -1z) = 0Subproblem 1
Set the factor '(4 + z)' equal to zero and attempt to solve: Simplifying 4 + z = 0 Solving 4 + z = 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 + z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + z = 0 + -4 z = 0 + -4 Combine like terms: 0 + -4 = -4 z = -4 Simplifying z = -4Subproblem 2
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 3
Set the factor '(7 + z)' equal to zero and attempt to solve: Simplifying 7 + z = 0 Solving 7 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + z = 0 + -7 z = 0 + -7 Combine like terms: 0 + -7 = -7 z = -7 Simplifying z = -7Subproblem 4
Set the factor '(7 + -1z)' equal to zero and attempt to solve: Simplifying 7 + -1z = 0 Solving 7 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1z = 0 + -7 -1z = 0 + -7 Combine like terms: 0 + -7 = -7 -1z = -7 Divide each side by '-1'. z = 7 Simplifying z = 7Solution
z = {-4, 4, -7, 7}
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