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Simplifying (2 + z)(2z + -3) = 0 Reorder the terms: (2 + z)(-3 + 2z) = 0 Multiply (2 + z) * (-3 + 2z) (2(-3 + 2z) + z(-3 + 2z)) = 0 ((-3 * 2 + 2z * 2) + z(-3 + 2z)) = 0 ((-6 + 4z) + z(-3 + 2z)) = 0 (-6 + 4z + (-3 * z + 2z * z)) = 0 (-6 + 4z + (-3z + 2z2)) = 0 Combine like terms: 4z + -3z = 1z (-6 + 1z + 2z2) = 0 Solving -6 + 1z + 2z2 = 0 Solving for variable 'z'. Factor a trinomial. (-2 + -1z)(3 + -2z) = 0Subproblem 1
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 = -2Subproblem 2
Set the factor '(3 + -2z)' equal to zero and attempt to solve: Simplifying 3 + -2z = 0 Solving 3 + -2z = 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 + -2z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2z = 0 + -3 -2z = 0 + -3 Combine like terms: 0 + -3 = -3 -2z = -3 Divide each side by '-2'. z = 1.5 Simplifying z = 1.5Solution
z = {-2, 1.5}
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