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Simplifying t4 + 6t2 + 9 = t2 + 3 + 12 Reorder the terms: 9 + 6t2 + t4 = t2 + 3 + 12 Reorder the terms: 9 + 6t2 + t4 = 3 + 12 + t2 Combine like terms: 3 + 12 = 15 9 + 6t2 + t4 = 15 + t2 Solving 9 + 6t2 + t4 = 15 + t2 Solving for variable 't'. Reorder the terms: 9 + -15 + 6t2 + -1t2 + t4 = 15 + t2 + -15 + -1t2 Combine like terms: 9 + -15 = -6 -6 + 6t2 + -1t2 + t4 = 15 + t2 + -15 + -1t2 Combine like terms: 6t2 + -1t2 = 5t2 -6 + 5t2 + t4 = 15 + t2 + -15 + -1t2 Reorder the terms: -6 + 5t2 + t4 = 15 + -15 + t2 + -1t2 Combine like terms: 15 + -15 = 0 -6 + 5t2 + t4 = 0 + t2 + -1t2 -6 + 5t2 + t4 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 -6 + 5t2 + t4 = 0 Factor a trinomial. (-6 + -1t2)(1 + -1t2) = 0 Factor a difference between two squares. (-6 + -1t2)((1 + t)(1 + -1t)) = 0Subproblem 1
Set the factor '(-6 + -1t2)' equal to zero and attempt to solve: Simplifying -6 + -1t2 = 0 Solving -6 + -1t2 = 0 Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1t2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1t2 = 0 + 6 -1t2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1t2 = 6 Divide each side by '-1'. t2 = -6 Simplifying t2 = -6 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 + t)' equal to zero and attempt to solve: Simplifying 1 + t = 0 Solving 1 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + t = 0 + -1 t = 0 + -1 Combine like terms: 0 + -1 = -1 t = -1 Simplifying t = -1Subproblem 3
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {-1, 1}
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