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Simplifying (z + -4)(z + -10) = 0 Reorder the terms: (-4 + z)(z + -10) = 0 Reorder the terms: (-4 + z)(-10 + z) = 0 Multiply (-4 + z) * (-10 + z) (-4(-10 + z) + z(-10 + z)) = 0 ((-10 * -4 + z * -4) + z(-10 + z)) = 0 ((40 + -4z) + z(-10 + z)) = 0 (40 + -4z + (-10 * z + z * z)) = 0 (40 + -4z + (-10z + z2)) = 0 Combine like terms: -4z + -10z = -14z (40 + -14z + z2) = 0 Solving 40 + -14z + z2 = 0 Solving for variable 'z'. Factor a trinomial. (4 + -1z)(10 + -1z) = 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 '(10 + -1z)' equal to zero and attempt to solve: Simplifying 10 + -1z = 0 Solving 10 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1z = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1z = 0 + -10 -1z = 0 + -10 Combine like terms: 0 + -10 = -10 -1z = -10 Divide each side by '-1'. z = 10 Simplifying z = 10Solution
z = {4, 10}
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