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Simplifying (6z + -7)(3z + -5) = 0 Reorder the terms: (-7 + 6z)(3z + -5) = 0 Reorder the terms: (-7 + 6z)(-5 + 3z) = 0 Multiply (-7 + 6z) * (-5 + 3z) (-7(-5 + 3z) + 6z * (-5 + 3z)) = 0 ((-5 * -7 + 3z * -7) + 6z * (-5 + 3z)) = 0 ((35 + -21z) + 6z * (-5 + 3z)) = 0 (35 + -21z + (-5 * 6z + 3z * 6z)) = 0 (35 + -21z + (-30z + 18z2)) = 0 Combine like terms: -21z + -30z = -51z (35 + -51z + 18z2) = 0 Solving 35 + -51z + 18z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + -6z)(5 + -3z) = 0Subproblem 1
Set the factor '(7 + -6z)' equal to zero and attempt to solve: Simplifying 7 + -6z = 0 Solving 7 + -6z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -6z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6z = 0 + -7 -6z = 0 + -7 Combine like terms: 0 + -7 = -7 -6z = -7 Divide each side by '-6'. z = 1.166666667 Simplifying z = 1.166666667Subproblem 2
Set the factor '(5 + -3z)' equal to zero and attempt to solve: Simplifying 5 + -3z = 0 Solving 5 + -3z = 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 + -3z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3z = 0 + -5 -3z = 0 + -5 Combine like terms: 0 + -5 = -5 -3z = -5 Divide each side by '-3'. z = 1.666666667 Simplifying z = 1.666666667Solution
z = {1.166666667, 1.666666667}
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