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Simplifying 2(3z + -5)(2z + -3) = 3z + -4 Reorder the terms: 2(-5 + 3z)(2z + -3) = 3z + -4 Reorder the terms: 2(-5 + 3z)(-3 + 2z) = 3z + -4 Multiply (-5 + 3z) * (-3 + 2z) 2(-5(-3 + 2z) + 3z * (-3 + 2z)) = 3z + -4 2((-3 * -5 + 2z * -5) + 3z * (-3 + 2z)) = 3z + -4 2((15 + -10z) + 3z * (-3 + 2z)) = 3z + -4 2(15 + -10z + (-3 * 3z + 2z * 3z)) = 3z + -4 2(15 + -10z + (-9z + 6z2)) = 3z + -4 Combine like terms: -10z + -9z = -19z 2(15 + -19z + 6z2) = 3z + -4 (15 * 2 + -19z * 2 + 6z2 * 2) = 3z + -4 (30 + -38z + 12z2) = 3z + -4 Reorder the terms: 30 + -38z + 12z2 = -4 + 3z Solving 30 + -38z + 12z2 = -4 + 3z Solving for variable 'z'. Reorder the terms: 30 + 4 + -38z + -3z + 12z2 = -4 + 3z + 4 + -3z Combine like terms: 30 + 4 = 34 34 + -38z + -3z + 12z2 = -4 + 3z + 4 + -3z Combine like terms: -38z + -3z = -41z 34 + -41z + 12z2 = -4 + 3z + 4 + -3z Reorder the terms: 34 + -41z + 12z2 = -4 + 4 + 3z + -3z Combine like terms: -4 + 4 = 0 34 + -41z + 12z2 = 0 + 3z + -3z 34 + -41z + 12z2 = 3z + -3z Combine like terms: 3z + -3z = 0 34 + -41z + 12z2 = 0 Factor a trinomial. (17 + -12z)(2 + -1z) = 0Subproblem 1
Set the factor '(17 + -12z)' equal to zero and attempt to solve: Simplifying 17 + -12z = 0 Solving 17 + -12z = 0 Move all terms containing z to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -12z = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -12z = 0 + -17 -12z = 0 + -17 Combine like terms: 0 + -17 = -17 -12z = -17 Divide each side by '-12'. z = 1.416666667 Simplifying z = 1.416666667Subproblem 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 = {1.416666667, 2}
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