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Simplifying 6z(2z + 3)(z + -7) = 0 Reorder the terms: 6z(3 + 2z)(z + -7) = 0 Reorder the terms: 6z(3 + 2z)(-7 + z) = 0 Multiply (3 + 2z) * (-7 + z) 6z(3(-7 + z) + 2z * (-7 + z)) = 0 6z((-7 * 3 + z * 3) + 2z * (-7 + z)) = 0 6z((-21 + 3z) + 2z * (-7 + z)) = 0 6z(-21 + 3z + (-7 * 2z + z * 2z)) = 0 6z(-21 + 3z + (-14z + 2z2)) = 0 Combine like terms: 3z + -14z = -11z 6z(-21 + -11z + 2z2) = 0 (-21 * 6z + -11z * 6z + 2z2 * 6z) = 0 (-126z + -66z2 + 12z3) = 0 Solving -126z + -66z2 + 12z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '6z'. 6z(-21 + -11z + 2z2) = 0 Factor a trinomial. 6z((-3 + -2z)(7 + -1z)) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(-3 + -2z)' equal to zero and attempt to solve: Simplifying -3 + -2z = 0 Solving -3 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2z = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2z = 0 + 3 -2z = 0 + 3 Combine like terms: 0 + 3 = 3 -2z = 3 Divide each side by '-2'. z = -1.5 Simplifying z = -1.5Subproblem 3
Set the factor '(7 + -1z)' equal to zero and attempt to solve: Simplifying 7 + -1z = 0 Solving 7 + -1z = 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 + -1z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1z = 0 + -7 -1z = 0 + -7 Combine like terms: 0 + -7 = -7 -1z = -7 Divide each side by '-1'. z = 7 Simplifying z = 7Solution
z = {0, -1.5, 7}
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