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Simplifying (z + -2)(z + 3) = z * 2 + 6 Reorder the terms: (-2 + z)(z + 3) = z * 2 + 6 Reorder the terms: (-2 + z)(3 + z) = z * 2 + 6 Multiply (-2 + z) * (3 + z) (-2(3 + z) + z(3 + z)) = z * 2 + 6 ((3 * -2 + z * -2) + z(3 + z)) = z * 2 + 6 ((-6 + -2z) + z(3 + z)) = z * 2 + 6 (-6 + -2z + (3 * z + z * z)) = z * 2 + 6 (-6 + -2z + (3z + z2)) = z * 2 + 6 Combine like terms: -2z + 3z = 1z (-6 + 1z + z2) = z * 2 + 6 Reorder the terms for easier multiplication: -6 + 1z + z2 = 2z + 6 Reorder the terms: -6 + 1z + z2 = 6 + 2z Solving -6 + 1z + z2 = 6 + 2z Solving for variable 'z'. Reorder the terms: -6 + -6 + 1z + -2z + z2 = 6 + 2z + -6 + -2z Combine like terms: -6 + -6 = -12 -12 + 1z + -2z + z2 = 6 + 2z + -6 + -2z Combine like terms: 1z + -2z = -1z -12 + -1z + z2 = 6 + 2z + -6 + -2z Reorder the terms: -12 + -1z + z2 = 6 + -6 + 2z + -2z Combine like terms: 6 + -6 = 0 -12 + -1z + z2 = 0 + 2z + -2z -12 + -1z + z2 = 2z + -2z Combine like terms: 2z + -2z = 0 -12 + -1z + z2 = 0 Factor a trinomial. (-3 + -1z)(4 + -1z) = 0Subproblem 1
Set the factor '(-3 + -1z)' equal to zero and attempt to solve: Simplifying -3 + -1z = 0 Solving -3 + -1z = 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 + -1z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1z = 0 + 3 -1z = 0 + 3 Combine like terms: 0 + 3 = 3 -1z = 3 Divide each side by '-1'. z = -3 Simplifying z = -3Subproblem 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Divide each side by '-1'. z = 4 Simplifying z = 4Solution
z = {-3, 4}
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