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Simplifying (7 + z)(3z + 2) = 0 Reorder the terms: (7 + z)(2 + 3z) = 0 Multiply (7 + z) * (2 + 3z) (7(2 + 3z) + z(2 + 3z)) = 0 ((2 * 7 + 3z * 7) + z(2 + 3z)) = 0 ((14 + 21z) + z(2 + 3z)) = 0 (14 + 21z + (2 * z + 3z * z)) = 0 (14 + 21z + (2z + 3z2)) = 0 Combine like terms: 21z + 2z = 23z (14 + 23z + 3z2) = 0 Solving 14 + 23z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (7 + z)(2 + 3z) = 0Subproblem 1
Set the factor '(7 + z)' equal to zero and attempt to solve: Simplifying 7 + z = 0 Solving 7 + z = 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 + z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + z = 0 + -7 z = 0 + -7 Combine like terms: 0 + -7 = -7 z = -7 Simplifying z = -7Subproblem 2
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 = -0.6666666667Solution
z = {-7, -0.6666666667}
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