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Simplifying (6z + -7)(3z + 2) = 0 Reorder the terms: (-7 + 6z)(3z + 2) = 0 Reorder the terms: (-7 + 6z)(2 + 3z) = 0 Multiply (-7 + 6z) * (2 + 3z) (-7(2 + 3z) + 6z * (2 + 3z)) = 0 ((2 * -7 + 3z * -7) + 6z * (2 + 3z)) = 0 ((-14 + -21z) + 6z * (2 + 3z)) = 0 (-14 + -21z + (2 * 6z + 3z * 6z)) = 0 (-14 + -21z + (12z + 18z2)) = 0 Combine like terms: -21z + 12z = -9z (-14 + -9z + 18z2) = 0 Solving -14 + -9z + 18z2 = 0 Solving for variable 'z'. Factor a trinomial. (-2 + -3z)(7 + -6z) = 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 '(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 = 1.166666667Solution
z = {-0.6666666667, 1.166666667}
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