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Simplifying (3z + -2)(2z + -5) = 0 Reorder the terms: (-2 + 3z)(2z + -5) = 0 Reorder the terms: (-2 + 3z)(-5 + 2z) = 0 Multiply (-2 + 3z) * (-5 + 2z) (-2(-5 + 2z) + 3z * (-5 + 2z)) = 0 ((-5 * -2 + 2z * -2) + 3z * (-5 + 2z)) = 0 ((10 + -4z) + 3z * (-5 + 2z)) = 0 (10 + -4z + (-5 * 3z + 2z * 3z)) = 0 (10 + -4z + (-15z + 6z2)) = 0 Combine like terms: -4z + -15z = -19z (10 + -19z + 6z2) = 0 Solving 10 + -19z + 6z2 = 0 Solving for variable 'z'. Factor a trinomial. (2 + -3z)(5 + -2z) = 0Subproblem 1
Set the factor '(2 + -3z)' equal to zero and attempt to solve: Simplifying 2 + -3z = 0 Solving 2 + -3z = 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 + -3z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3z = 0 + -2 -3z = 0 + -2 Combine like terms: 0 + -2 = -2 -3z = -2 Divide each side by '-3'. z = 0.6666666667 Simplifying z = 0.6666666667Subproblem 2
Set the factor '(5 + -2z)' equal to zero and attempt to solve: Simplifying 5 + -2z = 0 Solving 5 + -2z = 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 + -2z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2z = 0 + -5 -2z = 0 + -5 Combine like terms: 0 + -5 = -5 -2z = -5 Divide each side by '-2'. z = 2.5 Simplifying z = 2.5Solution
z = {0.6666666667, 2.5}
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