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Simplifying z + -4z(z + 2) = -6 + -2z Reorder the terms: z + -4z(2 + z) = -6 + -2z z + (2 * -4z + z * -4z) = -6 + -2z z + (-8z + -4z2) = -6 + -2z Combine like terms: z + -8z = -7z -7z + -4z2 = -6 + -2z Solving -7z + -4z2 = -6 + -2z Solving for variable 'z'. Reorder the terms: 6 + -7z + 2z + -4z2 = -6 + -2z + 6 + 2z Combine like terms: -7z + 2z = -5z 6 + -5z + -4z2 = -6 + -2z + 6 + 2z Reorder the terms: 6 + -5z + -4z2 = -6 + 6 + -2z + 2z Combine like terms: -6 + 6 = 0 6 + -5z + -4z2 = 0 + -2z + 2z 6 + -5z + -4z2 = -2z + 2z Combine like terms: -2z + 2z = 0 6 + -5z + -4z2 = 0 Factor a trinomial. (3 + -4z)(2 + z) = 0Subproblem 1
Set the factor '(3 + -4z)' equal to zero and attempt to solve: Simplifying 3 + -4z = 0 Solving 3 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4z = 0 + -3 -4z = 0 + -3 Combine like terms: 0 + -3 = -3 -4z = -3 Divide each side by '-4'. z = 0.75 Simplifying z = 0.75Subproblem 2
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 = -2Solution
z = {0.75, -2}
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