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Simplifying 3t4 + -12t2 + 4t2 + -16 = 0 Reorder the terms: -16 + -12t2 + 4t2 + 3t4 = 0 Combine like terms: -12t2 + 4t2 = -8t2 -16 + -8t2 + 3t4 = 0 Solving -16 + -8t2 + 3t4 = 0 Solving for variable 't'. Factor a trinomial. (-4 + -3t2)(4 + -1t2) = 0 Factor a difference between two squares. (-4 + -3t2)((2 + t)(2 + -1t)) = 0Subproblem 1
Set the factor '(-4 + -3t2)' equal to zero and attempt to solve: Simplifying -4 + -3t2 = 0 Solving -4 + -3t2 = 0 Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3t2 = 0 + 4 -3t2 = 0 + 4 Combine like terms: 0 + 4 = 4 -3t2 = 4 Divide each side by '-3'. t2 = -1.333333333 Simplifying t2 = -1.333333333 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 '(2 + t)' equal to zero and attempt to solve: Simplifying 2 + t = 0 Solving 2 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + t = 0 + -2 t = 0 + -2 Combine like terms: 0 + -2 = -2 t = -2 Simplifying t = -2Subproblem 3
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {-2, 2}
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