40=8t(7-2t)

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Solution for 40=8t(7-2t) equation:


Simplifying
40 = 8t(7 + -2t)
40 = (7 * 8t + -2t * 8t)
40 = (56t + -16t2)

Solving
40 = 56t + -16t2

Solving for variable 't'.

Reorder the terms:
40 + -56t + 16t2 = 56t + -56t + -16t2 + 16t2

Combine like terms: 56t + -56t = 0
40 + -56t + 16t2 = 0 + -16t2 + 16t2
40 + -56t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
40 + -56t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(5 + -7t + 2t2) = 0

Factor a trinomial.
8((1 + -1t)(5 + -2t)) = 0

Ignore the factor 8.

Subproblem 1

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 = 1

Subproblem 2

Set the factor '(5 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 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 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5

Solution

t = {1, 2.5}

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