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Simplifying (3x2 + 1)(4x2 + 5) = 0 Reorder the terms: (1 + 3x2)(4x2 + 5) = 0 Reorder the terms: (1 + 3x2)(5 + 4x2) = 0 Multiply (1 + 3x2) * (5 + 4x2) (1(5 + 4x2) + 3x2 * (5 + 4x2)) = 0 ((5 * 1 + 4x2 * 1) + 3x2 * (5 + 4x2)) = 0 ((5 + 4x2) + 3x2 * (5 + 4x2)) = 0 (5 + 4x2 + (5 * 3x2 + 4x2 * 3x2)) = 0 (5 + 4x2 + (15x2 + 12x4)) = 0 Combine like terms: 4x2 + 15x2 = 19x2 (5 + 19x2 + 12x4) = 0 Solving 5 + 19x2 + 12x4 = 0 Solving for variable 'x'. Factor a trinomial. (5 + 4x2)(1 + 3x2) = 0Subproblem 1
Set the factor '(5 + 4x2)' equal to zero and attempt to solve: Simplifying 5 + 4x2 = 0 Solving 5 + 4x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x2 = 0 + -5 4x2 = 0 + -5 Combine like terms: 0 + -5 = -5 4x2 = -5 Divide each side by '4'. x2 = -1.25 Simplifying x2 = -1.25 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 + 3x2)' equal to zero and attempt to solve: Simplifying 1 + 3x2 = 0 Solving 1 + 3x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x2 = 0 + -1 3x2 = 0 + -1 Combine like terms: 0 + -1 = -1 3x2 = -1 Divide each side by '3'. x2 = -0.3333333333 Simplifying x2 = -0.3333333333 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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