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Simplifying z2 + 6z + -307 = 8 Reorder the terms: -307 + 6z + z2 = 8 Solving -307 + 6z + z2 = 8 Solving for variable 'z'. Reorder the terms: -307 + -8 + 6z + z2 = 8 + -8 Combine like terms: -307 + -8 = -315 -315 + 6z + z2 = 8 + -8 Combine like terms: 8 + -8 = 0 -315 + 6z + z2 = 0 Factor a trinomial. (-21 + -1z)(15 + -1z) = 0Subproblem 1
Set the factor '(-21 + -1z)' equal to zero and attempt to solve: Simplifying -21 + -1z = 0 Solving -21 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + -1z = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -1z = 0 + 21 -1z = 0 + 21 Combine like terms: 0 + 21 = 21 -1z = 21 Divide each side by '-1'. z = -21 Simplifying z = -21Subproblem 2
Set the factor '(15 + -1z)' equal to zero and attempt to solve: Simplifying 15 + -1z = 0 Solving 15 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1z = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1z = 0 + -15 -1z = 0 + -15 Combine like terms: 0 + -15 = -15 -1z = -15 Divide each side by '-1'. z = 15 Simplifying z = 15Solution
z = {-21, 15}
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