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Simplifying 3t6 + -48t2 = 0 Reorder the terms: -48t2 + 3t6 = 0 Solving -48t2 + 3t6 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3t2'. 3t2(-16 + t4) = 0 Factor a difference between two squares. 3t2((4 + t2)(-4 + t2)) = 0 Factor a difference between two squares. 3t2((4 + t2)((2 + t)(-2 + t))) = 0 Ignore the factor 3.Subproblem 1
Set the factor 't2' equal to zero and attempt to solve: Simplifying t2 = 0 Solving t2 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t2 = 0 Take the square root of each side: t = {0}Subproblem 2
Set the factor '(4 + t2)' equal to zero and attempt to solve: Simplifying 4 + t2 = 0 Solving 4 + t2 = 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 + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + t2 = 0 + -4 t2 = 0 + -4 Combine like terms: 0 + -4 = -4 t2 = -4 Simplifying t2 = -4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
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 4
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 = 2Solution
t = {0, -2, 2}
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