40=-2t^2+16t+16

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Solution for 40=-2t^2+16t+16 equation:


Simplifying
40 = -2t2 + 16t + 16

Reorder the terms:
40 = 16 + 16t + -2t2

Solving
40 = 16 + 16t + -2t2

Solving for variable 't'.

Combine like terms: 40 + -16 = 24
24 + -16t + 2t2 = 16 + 16t + -2t2 + -16 + -16t + 2t2

Reorder the terms:
24 + -16t + 2t2 = 16 + -16 + 16t + -16t + -2t2 + 2t2

Combine like terms: 16 + -16 = 0
24 + -16t + 2t2 = 0 + 16t + -16t + -2t2 + 2t2
24 + -16t + 2t2 = 16t + -16t + -2t2 + 2t2

Combine like terms: 16t + -16t = 0
24 + -16t + 2t2 = 0 + -2t2 + 2t2
24 + -16t + 2t2 = -2t2 + 2t2

Combine like terms: -2t2 + 2t2 = 0
24 + -16t + 2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -8t + t2) = 0

Factor a trinomial.
2((2 + -1t)(6 + -1t)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2

Subproblem 2

Set the factor '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6

Solution

t = {2, 6}

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