546=8t^2+8t+450

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Solution for 546=8t^2+8t+450 equation:


Simplifying
546 = 8t2 + 8t + 450

Reorder the terms:
546 = 450 + 8t + 8t2

Solving
546 = 450 + 8t + 8t2

Solving for variable 't'.

Combine like terms: 546 + -450 = 96
96 + -8t + -8t2 = 450 + 8t + 8t2 + -450 + -8t + -8t2

Reorder the terms:
96 + -8t + -8t2 = 450 + -450 + 8t + -8t + 8t2 + -8t2

Combine like terms: 450 + -450 = 0
96 + -8t + -8t2 = 0 + 8t + -8t + 8t2 + -8t2
96 + -8t + -8t2 = 8t + -8t + 8t2 + -8t2

Combine like terms: 8t + -8t = 0
96 + -8t + -8t2 = 0 + 8t2 + -8t2
96 + -8t + -8t2 = 8t2 + -8t2

Combine like terms: 8t2 + -8t2 = 0
96 + -8t + -8t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(12 + -1t + -1t2) = 0

Factor a trinomial.
8((3 + -1t)(4 + t)) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3

Subproblem 2

Set the factor '(4 + t)' equal to zero and attempt to solve: Simplifying 4 + t = 0 Solving 4 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + t = 0 + -4 t = 0 + -4 Combine like terms: 0 + -4 = -4 t = -4 Simplifying t = -4

Solution

t = {3, -4}

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