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Simplifying (3z + 1)(2z + -5) = -5 Reorder the terms: (1 + 3z)(2z + -5) = -5 Reorder the terms: (1 + 3z)(-5 + 2z) = -5 Multiply (1 + 3z) * (-5 + 2z) (1(-5 + 2z) + 3z * (-5 + 2z)) = -5 ((-5 * 1 + 2z * 1) + 3z * (-5 + 2z)) = -5 ((-5 + 2z) + 3z * (-5 + 2z)) = -5 (-5 + 2z + (-5 * 3z + 2z * 3z)) = -5 (-5 + 2z + (-15z + 6z2)) = -5 Combine like terms: 2z + -15z = -13z (-5 + -13z + 6z2) = -5 Add '5' to each side of the equation. -5 + -13z + 5 + 6z2 = -5 + 5 Reorder the terms: -5 + 5 + -13z + 6z2 = -5 + 5 Combine like terms: -5 + 5 = 0 0 + -13z + 6z2 = -5 + 5 -13z + 6z2 = -5 + 5 Combine like terms: -5 + 5 = 0 -13z + 6z2 = 0 Solving -13z + 6z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), 'z'. z(-13 + 6z) = 0Subproblem 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 '(-13 + 6z)' equal to zero and attempt to solve: Simplifying -13 + 6z = 0 Solving -13 + 6z = 0 Move all terms containing z to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 6z = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 6z = 0 + 13 6z = 0 + 13 Combine like terms: 0 + 13 = 13 6z = 13 Divide each side by '6'. z = 2.166666667 Simplifying z = 2.166666667Solution
z = {0, 2.166666667}
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