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Simplifying (5t + -4)(3t + -4) = at2 + bt + c Reorder the terms: (-4 + 5t)(3t + -4) = at2 + bt + c Reorder the terms: (-4 + 5t)(-4 + 3t) = at2 + bt + c Multiply (-4 + 5t) * (-4 + 3t) (-4(-4 + 3t) + 5t * (-4 + 3t)) = at2 + bt + c ((-4 * -4 + 3t * -4) + 5t * (-4 + 3t)) = at2 + bt + c ((16 + -12t) + 5t * (-4 + 3t)) = at2 + bt + c (16 + -12t + (-4 * 5t + 3t * 5t)) = at2 + bt + c (16 + -12t + (-20t + 15t2)) = at2 + bt + c Combine like terms: -12t + -20t = -32t (16 + -32t + 15t2) = at2 + bt + c Solving 16 + -32t + 15t2 = at2 + bt + c Solving for variable 't'. Reorder the terms: 16 + -1at2 + -1bt + -1c + -32t + 15t2 = at2 + bt + c + -1at2 + -1bt + -1c Reorder the terms: 16 + -1at2 + -1bt + -1c + -32t + 15t2 = at2 + -1at2 + bt + -1bt + c + -1c Combine like terms: at2 + -1at2 = 0 16 + -1at2 + -1bt + -1c + -32t + 15t2 = 0 + bt + -1bt + c + -1c 16 + -1at2 + -1bt + -1c + -32t + 15t2 = bt + -1bt + c + -1c Combine like terms: bt + -1bt = 0 16 + -1at2 + -1bt + -1c + -32t + 15t2 = 0 + c + -1c 16 + -1at2 + -1bt + -1c + -32t + 15t2 = c + -1c Combine like terms: c + -1c = 0 16 + -1at2 + -1bt + -1c + -32t + 15t2 = 0 The solution to this equation could not be determined.
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