Simplifying(7z + 9)(z + 7) = 47Reorder the terms

9 + 7z)(z + 7) = 47Reorder the terms

9 + 7z)(7 + z) = 47Multiply (9 + 7z) * (7 + z)(9(7 + z) + 7z * (7 + z)) = 47((7 * 9 + z * 9) + 7z * (7 + z)) = 47((63 + 9z) + 7z * (7 + z)) = 47(63 + 9z + (7 * 7z + z * 7z)) = 47(63 + 9z + (49z + 7z2)) = 47Combine like terms: 9z + 49z = 58z(63 + 58z + 7z2) = 47Solving63 + 58z + 7z2 = 47Solving for variable 'z'.Reorder the terms:63 + -47 + 58z + 7z2 = 47 + -47Combine like terms: 63 + -47 = 1616 + 58z + 7z2 = 47 + -47Combine like terms: 47 + -47 = 016 + 58z + 7z2 = 0Factor a trinomial.(8 + z)(2 + 7z) = 0Subproblem 1Set the factor '(8 + z)' equal to zero and attempt to solve:Simplifying8 + z = 0Solving8 + z = 0Move all terms containing z to the left, all other terms to the right.Add '-8' to each side of the equation.8 + -8 + z = 0 + -8Combine like terms: 8 + -8 = 00 + z = 0 + -8z = 0 + -8Combine like terms: 0 + -8 = -8z = -8Simplifyingz = -8Subproblem 2Set the factor '(2 + 7z)' equal to zero and attempt to solve:Simplifying2 + 7z = 0Solving2 + 7z = 0Move all terms containing z to the left, all other terms to the right.Add '-2' to each side of the equation.2 + -2 + 7z = 0 + -2Combine like terms: 2 + -2 = 00 + 7z = 0 + -27z = 0 + -2Combine like terms: 0 + -2 = -27z = -2Divide each side by '7'.z = -0.2857142857Simplifyingz = -0.2857142857Solutionz = {-8, -0.2857142857}