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Simplifying z(3z + 11) = 20 Reorder the terms: z(11 + 3z) = 20 (11 * z + 3z * z) = 20 (11z + 3z2) = 20 Solving 11z + 3z2 = 20 Solving for variable 'z'. Reorder the terms: -20 + 11z + 3z2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 11z + 3z2 = 0 Factor a trinomial. (-5 + -1z)(4 + -3z) = 0Subproblem 1
Set the factor '(-5 + -1z)' equal to zero and attempt to solve: Simplifying -5 + -1z = 0 Solving -5 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1z = 0 + 5 -1z = 0 + 5 Combine like terms: 0 + 5 = 5 -1z = 5 Divide each side by '-1'. z = -5 Simplifying z = -5Subproblem 2
Set the factor '(4 + -3z)' equal to zero and attempt to solve: Simplifying 4 + -3z = 0 Solving 4 + -3z = 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 + -3z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3z = 0 + -4 -3z = 0 + -4 Combine like terms: 0 + -4 = -4 -3z = -4 Divide each side by '-3'. z = 1.333333333 Simplifying z = 1.333333333Solution
z = {-5, 1.333333333}
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