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Simplifying -2 = z2 + 3z Reorder the terms: -2 = 3z + z2 Solving -2 = 3z + z2 Solving for variable 'z'. Reorder the terms: -2 + -3z + -1z2 = 3z + -3z + z2 + -1z2 Combine like terms: 3z + -3z = 0 -2 + -3z + -1z2 = 0 + z2 + -1z2 -2 + -3z + -1z2 = z2 + -1z2 Combine like terms: z2 + -1z2 = 0 -2 + -3z + -1z2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 3z + z2) = 0 Factor a trinomial. -1((2 + z)(1 + z)) = 0 Ignore the factor -1.Subproblem 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 '(1 + z)' equal to zero and attempt to solve: Simplifying 1 + z = 0 Solving 1 + z = 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 + z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z = 0 + -1 z = 0 + -1 Combine like terms: 0 + -1 = -1 z = -1 Simplifying z = -1Solution
z = {-2, -1}
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