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Simplifying (4z2) + -1(12z) + -7 = 0 Remove parenthesis around (12z) (4z2) + -1 * 12z + -7 = 0 Multiply -1 * 12 (4z2) + -12z + -7 = 0 Reorder the terms: -7 + -12z + (4z2) = 0 Solving -7 + -12z + (4z2) = 0 Solving for variable 'z'. Factor a trinomial. (-1 + -2z)(7 + -2z) = 0Subproblem 1
Set the factor '(-1 + -2z)' equal to zero and attempt to solve: Simplifying -1 + -2z = 0 Solving -1 + -2z = 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 + -2z = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2z = 0 + 1 -2z = 0 + 1 Combine like terms: 0 + 1 = 1 -2z = 1 Divide each side by '-2'. z = -0.5 Simplifying z = -0.5Subproblem 2
Set the factor '(7 + -2z)' equal to zero and attempt to solve: Simplifying 7 + -2z = 0 Solving 7 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2z = 0 + -7 -2z = 0 + -7 Combine like terms: 0 + -7 = -7 -2z = -7 Divide each side by '-2'. z = 3.5 Simplifying z = 3.5Solution
z = {-0.5, 3.5}
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