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Simplifying -27t4 + 42t3 + 5t2 = 0 Reorder the terms: 5t2 + 42t3 + -27t4 = 0 Solving 5t2 + 42t3 + -27t4 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't2'. t2(5 + 42t + -27t2) = 0 Factor a trinomial. t2((5 + -3t)(1 + 9t)) = 0Subproblem 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 '(5 + -3t)' equal to zero and attempt to solve: Simplifying 5 + -3t = 0 Solving 5 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3t = 0 + -5 -3t = 0 + -5 Combine like terms: 0 + -5 = -5 -3t = -5 Divide each side by '-3'. t = 1.666666667 Simplifying t = 1.666666667Subproblem 3
Set the factor '(1 + 9t)' equal to zero and attempt to solve: Simplifying 1 + 9t = 0 Solving 1 + 9t = 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 + 9t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 9t = 0 + -1 9t = 0 + -1 Combine like terms: 0 + -1 = -1 9t = -1 Divide each side by '9'. t = -0.1111111111 Simplifying t = -0.1111111111Solution
t = {0, 1.666666667, -0.1111111111}
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