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Simplifying (5z + -1)(2z + 3) = 3z + -3 Reorder the terms: (-1 + 5z)(2z + 3) = 3z + -3 Reorder the terms: (-1 + 5z)(3 + 2z) = 3z + -3 Multiply (-1 + 5z) * (3 + 2z) (-1(3 + 2z) + 5z * (3 + 2z)) = 3z + -3 ((3 * -1 + 2z * -1) + 5z * (3 + 2z)) = 3z + -3 ((-3 + -2z) + 5z * (3 + 2z)) = 3z + -3 (-3 + -2z + (3 * 5z + 2z * 5z)) = 3z + -3 (-3 + -2z + (15z + 10z2)) = 3z + -3 Combine like terms: -2z + 15z = 13z (-3 + 13z + 10z2) = 3z + -3 Reorder the terms: -3 + 13z + 10z2 = -3 + 3z Add '3' to each side of the equation. -3 + 13z + 3 + 10z2 = -3 + 3 + 3z Reorder the terms: -3 + 3 + 13z + 10z2 = -3 + 3 + 3z Combine like terms: -3 + 3 = 0 0 + 13z + 10z2 = -3 + 3 + 3z 13z + 10z2 = -3 + 3 + 3z Combine like terms: -3 + 3 = 0 13z + 10z2 = 0 + 3z 13z + 10z2 = 3z Solving 13z + 10z2 = 3z Solving for variable 'z'. Reorder the terms: 13z + -3z + 10z2 = 3z + -3z Combine like terms: 13z + -3z = 10z 10z + 10z2 = 3z + -3z Combine like terms: 3z + -3z = 0 10z + 10z2 = 0 Factor out the Greatest Common Factor (GCF), '10z'. 10z(1 + z) = 0 Ignore the factor 10.Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(1 + z)' equal to zero and attempt to solve: Simplifying 1 + z = 0 Solving 1 + z = 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 + z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z = 0 + -1 z = 0 + -1 Combine like terms: 0 + -1 = -1 z = -1 Simplifying z = -1Solution
z = {0, -1}
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