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Simplifying (3z + -6)(2z + 10) = 0 Reorder the terms: (-6 + 3z)(2z + 10) = 0 Reorder the terms: (-6 + 3z)(10 + 2z) = 0 Multiply (-6 + 3z) * (10 + 2z) (-6(10 + 2z) + 3z * (10 + 2z)) = 0 ((10 * -6 + 2z * -6) + 3z * (10 + 2z)) = 0 ((-60 + -12z) + 3z * (10 + 2z)) = 0 (-60 + -12z + (10 * 3z + 2z * 3z)) = 0 (-60 + -12z + (30z + 6z2)) = 0 Combine like terms: -12z + 30z = 18z (-60 + 18z + 6z2) = 0 Solving -60 + 18z + 6z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '6'. 6(-10 + 3z + z2) = 0 Factor a trinomial. 6((-5 + -1z)(2 + -1z)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-5 + -1z)' equal to zero and attempt to solve: Simplifying -5 + -1z = 0 Solving -5 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1z = 0 + 5 -1z = 0 + 5 Combine like terms: 0 + 5 = 5 -1z = 5 Divide each side by '-1'. z = -5 Simplifying z = -5Subproblem 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 = {-5, 2}
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