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Simplifying 12f2 + -75ft + -63t2 = 0 Reorder the terms: -75ft + 12f2 + -63t2 = 0 Solving -75ft + 12f2 + -63t2 = 0 Solving for variable 'f'. Factor out the Greatest Common Factor (GCF), '3'. 3(-25ft + 4f2 + -21t2) = 0 Factor a trinomial. 3((f + -7t)(4f + 3t)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(f + -7t)' equal to zero and attempt to solve: Simplifying f + -7t = 0 Solving f + -7t = 0 Move all terms containing f to the left, all other terms to the right. Add '7t' to each side of the equation. f + -7t + 7t = 0 + 7t Combine like terms: -7t + 7t = 0 f + 0 = 0 + 7t f = 0 + 7t Remove the zero: f = 7t Simplifying f = 7tSubproblem 2
Set the factor '(4f + 3t)' equal to zero and attempt to solve: Simplifying 4f + 3t = 0 Solving 4f + 3t = 0 Move all terms containing f to the left, all other terms to the right. Add '-3t' to each side of the equation. 4f + 3t + -3t = 0 + -3t Combine like terms: 3t + -3t = 0 4f + 0 = 0 + -3t 4f = 0 + -3t Remove the zero: 4f = -3t Divide each side by '4'. f = -0.75t Simplifying f = -0.75tSolution
f = {7t, -0.75t}
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