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Simplifying (t4) + -1(4t3) + -1(5t2) = 0 t4 + -1(4t3) + -1(5t2) = 0 Remove parenthesis around (4t3) t4 + -1 * 4t3 + -1(5t2) = 0 Multiply -1 * 4 t4 + -4t3 + -1(5t2) = 0 Remove parenthesis around (5t2) t4 + -4t3 + -1 * 5t2 = 0 Multiply -1 * 5 t4 + -4t3 + -5t2 = 0 Reorder the terms: -5t2 + -4t3 + t4 = 0 Solving -5t2 + -4t3 + t4 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't2'. t2(-5 + -4t + t2) = 0 Factor a trinomial. t2((-1 + -1t)(5 + -1t)) = 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 '(-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 = -1Subproblem 3
Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 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 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Solution
t = {0, -1, 5}
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