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Simplifying (z2 + -4)(z2 + -9) = 0 Reorder the terms: (-4 + z2)(z2 + -9) = 0 Reorder the terms: (-4 + z2)(-9 + z2) = 0 Multiply (-4 + z2) * (-9 + z2) (-4(-9 + z2) + z2(-9 + z2)) = 0 ((-9 * -4 + z2 * -4) + z2(-9 + z2)) = 0 ((36 + -4z2) + z2(-9 + z2)) = 0 (36 + -4z2 + (-9 * z2 + z2 * z2)) = 0 (36 + -4z2 + (-9z2 + z4)) = 0 Combine like terms: -4z2 + -9z2 = -13z2 (36 + -13z2 + z4) = 0 Solving 36 + -13z2 + z4 = 0 Solving for variable 'z'. Factor a trinomial. (4 + -1z2)(9 + -1z2) = 0 Factor a difference between two squares. ((2 + z)(2 + -1z))(9 + -1z2) = 0 Factor a difference between two squares. ((3 + z)(3 + -1z))(2 + z)(2 + -1z) = 0Subproblem 1
Set the factor '(2 + z)' equal to zero and attempt to solve: Simplifying 2 + z = 0 Solving 2 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + z = 0 + -2 z = 0 + -2 Combine like terms: 0 + -2 = -2 z = -2 Simplifying z = -2Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Subproblem 3
Set the factor '(3 + z)' equal to zero and attempt to solve: Simplifying 3 + z = 0 Solving 3 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + z = 0 + -3 z = 0 + -3 Combine like terms: 0 + -3 = -3 z = -3 Simplifying z = -3Subproblem 4
Set the factor '(3 + -1z)' equal to zero and attempt to solve: Simplifying 3 + -1z = 0 Solving 3 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1z = 0 + -3 -1z = 0 + -3 Combine like terms: 0 + -3 = -3 -1z = -3 Divide each side by '-1'. z = 3 Simplifying z = 3Solution
z = {-2, 2, -3, 3}
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