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Simplifying -5t2 + 32t + 3 = 3t + 3 Reorder the terms: 3 + 32t + -5t2 = 3t + 3 Reorder the terms: 3 + 32t + -5t2 = 3 + 3t Add '-3' to each side of the equation. 3 + 32t + -3 + -5t2 = 3 + -3 + 3t Reorder the terms: 3 + -3 + 32t + -5t2 = 3 + -3 + 3t Combine like terms: 3 + -3 = 0 0 + 32t + -5t2 = 3 + -3 + 3t 32t + -5t2 = 3 + -3 + 3t Combine like terms: 3 + -3 = 0 32t + -5t2 = 0 + 3t 32t + -5t2 = 3t Solving 32t + -5t2 = 3t Solving for variable 't'. Reorder the terms: 32t + -3t + -5t2 = 3t + -3t Combine like terms: 32t + -3t = 29t 29t + -5t2 = 3t + -3t Combine like terms: 3t + -3t = 0 29t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(29 + -5t) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(29 + -5t)' equal to zero and attempt to solve: Simplifying 29 + -5t = 0 Solving 29 + -5t = 0 Move all terms containing t to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + -5t = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -5t = 0 + -29 -5t = 0 + -29 Combine like terms: 0 + -29 = -29 -5t = -29 Divide each side by '-5'. t = 5.8 Simplifying t = 5.8Solution
t = {0, 5.8}
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