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Simplifying (z + 11)(z + -4) = 0 Reorder the terms: (11 + z)(z + -4) = 0 Reorder the terms: (11 + z)(-4 + z) = 0 Multiply (11 + z) * (-4 + z) (11(-4 + z) + z(-4 + z)) = 0 ((-4 * 11 + z * 11) + z(-4 + z)) = 0 ((-44 + 11z) + z(-4 + z)) = 0 (-44 + 11z + (-4 * z + z * z)) = 0 (-44 + 11z + (-4z + z2)) = 0 Combine like terms: 11z + -4z = 7z (-44 + 7z + z2) = 0 Solving -44 + 7z + z2 = 0 Solving for variable 'z'. Factor a trinomial. (-11 + -1z)(4 + -1z) = 0Subproblem 1
Set the factor '(-11 + -1z)' equal to zero and attempt to solve: Simplifying -11 + -1z = 0 Solving -11 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1z = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1z = 0 + 11 -1z = 0 + 11 Combine like terms: 0 + 11 = 11 -1z = 11 Divide each side by '-1'. z = -11 Simplifying z = -11Subproblem 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 = 4Solution
z = {-11, 4}
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