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Simplifying 4t(3t2 + -4t) + -1t(7t) = 0 Reorder the terms: 4t(-4t + 3t2) + -1t(7t) = 0 (-4t * 4t + 3t2 * 4t) + -1t(7t) = 0 (-16t2 + 12t3) + -1t(7t) = 0 Remove parenthesis around (7t) -16t2 + 12t3 + -1t * 7t = 0 Reorder the terms for easier multiplication: -16t2 + 12t3 + -1 * 7t * t = 0 Multiply -1 * 7 -16t2 + 12t3 + -7t * t = 0 Multiply t * t -16t2 + 12t3 + -7t2 = 0 Reorder the terms: -16t2 + -7t2 + 12t3 = 0 Combine like terms: -16t2 + -7t2 = -23t2 -23t2 + 12t3 = 0 Solving -23t2 + 12t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't2'. t2(-23 + 12t) = 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 '(-23 + 12t)' equal to zero and attempt to solve: Simplifying -23 + 12t = 0 Solving -23 + 12t = 0 Move all terms containing t to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + 12t = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 12t = 0 + 23 12t = 0 + 23 Combine like terms: 0 + 23 = 23 12t = 23 Divide each side by '12'. t = 1.916666667 Simplifying t = 1.916666667Solution
t = {0, 1.916666667}
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