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Simplifying (4z2 + 1)(2 + 3z2) = 0 Reorder the terms: (1 + 4z2)(2 + 3z2) = 0 Multiply (1 + 4z2) * (2 + 3z2) (1(2 + 3z2) + 4z2 * (2 + 3z2)) = 0 ((2 * 1 + 3z2 * 1) + 4z2 * (2 + 3z2)) = 0 ((2 + 3z2) + 4z2 * (2 + 3z2)) = 0 (2 + 3z2 + (2 * 4z2 + 3z2 * 4z2)) = 0 (2 + 3z2 + (8z2 + 12z4)) = 0 Combine like terms: 3z2 + 8z2 = 11z2 (2 + 11z2 + 12z4) = 0 Solving 2 + 11z2 + 12z4 = 0 Solving for variable 'z'. Factor a trinomial. (2 + 3z2)(1 + 4z2) = 0Subproblem 1
Set the factor '(2 + 3z2)' equal to zero and attempt to solve: Simplifying 2 + 3z2 = 0 Solving 2 + 3z2 = 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 + 3z2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3z2 = 0 + -2 3z2 = 0 + -2 Combine like terms: 0 + -2 = -2 3z2 = -2 Divide each side by '3'. z2 = -0.6666666667 Simplifying z2 = -0.6666666667 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + 4z2)' equal to zero and attempt to solve: Simplifying 1 + 4z2 = 0 Solving 1 + 4z2 = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4z2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4z2 = 0 + -1 4z2 = 0 + -1 Combine like terms: 0 + -1 = -1 4z2 = -1 Divide each side by '4'. z2 = -0.25 Simplifying z2 = -0.25 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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