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Simplifying (z + 10)(z + -3) + 12 = 0 Reorder the terms: (10 + z)(z + -3) + 12 = 0 Reorder the terms: (10 + z)(-3 + z) + 12 = 0 Multiply (10 + z) * (-3 + z) (10(-3 + z) + z(-3 + z)) + 12 = 0 ((-3 * 10 + z * 10) + z(-3 + z)) + 12 = 0 ((-30 + 10z) + z(-3 + z)) + 12 = 0 (-30 + 10z + (-3 * z + z * z)) + 12 = 0 (-30 + 10z + (-3z + z2)) + 12 = 0 Combine like terms: 10z + -3z = 7z (-30 + 7z + z2) + 12 = 0 Reorder the terms: -30 + 12 + 7z + z2 = 0 Combine like terms: -30 + 12 = -18 -18 + 7z + z2 = 0 Solving -18 + 7z + z2 = 0 Solving for variable 'z'. Factor a trinomial. (-9 + -1z)(2 + -1z) = 0Subproblem 1
Set the factor '(-9 + -1z)' equal to zero and attempt to solve: Simplifying -9 + -1z = 0 Solving -9 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1z = 0 + 9 -1z = 0 + 9 Combine like terms: 0 + 9 = 9 -1z = 9 Divide each side by '-1'. z = -9 Simplifying z = -9Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 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 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Solution
z = {-9, 2}
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