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Simplifying (4z2 + 4z + -10) + (-13z2 + -19z + 6) = 0 Reorder the terms: (-10 + 4z + 4z2) + (-13z2 + -19z + 6) = 0 Remove parenthesis around (-10 + 4z + 4z2) -10 + 4z + 4z2 + (-13z2 + -19z + 6) = 0 Reorder the terms: -10 + 4z + 4z2 + (6 + -19z + -13z2) = 0 Remove parenthesis around (6 + -19z + -13z2) -10 + 4z + 4z2 + 6 + -19z + -13z2 = 0 Reorder the terms: -10 + 6 + 4z + -19z + 4z2 + -13z2 = 0 Combine like terms: -10 + 6 = -4 -4 + 4z + -19z + 4z2 + -13z2 = 0 Combine like terms: 4z + -19z = -15z -4 + -15z + 4z2 + -13z2 = 0 Combine like terms: 4z2 + -13z2 = -9z2 -4 + -15z + -9z2 = 0 Solving -4 + -15z + -9z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 15z + 9z2) = 0 Factor a trinomial. -1((4 + 3z)(1 + 3z)) = 0 Ignore the factor -1.Subproblem 1
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 = -1.333333333Subproblem 2
Set the factor '(1 + 3z)' equal to zero and attempt to solve: Simplifying 1 + 3z = 0 Solving 1 + 3z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3z = 0 + -1 3z = 0 + -1 Combine like terms: 0 + -1 = -1 3z = -1 Divide each side by '3'. z = -0.3333333333 Simplifying z = -0.3333333333Solution
z = {-1.333333333, -0.3333333333}
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