0=-10t^2+12t+54

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Solution for 0=-10t^2+12t+54 equation:


Simplifying
0 = -10t2 + 12t + 54

Reorder the terms:
0 = 54 + 12t + -10t2

Solving
0 = 54 + 12t + -10t2

Solving for variable 't'.

Combine like terms: 0 + -54 = -54
-54 + -12t + 10t2 = 54 + 12t + -10t2 + -54 + -12t + 10t2

Reorder the terms:
-54 + -12t + 10t2 = 54 + -54 + 12t + -12t + -10t2 + 10t2

Combine like terms: 54 + -54 = 0
-54 + -12t + 10t2 = 0 + 12t + -12t + -10t2 + 10t2
-54 + -12t + 10t2 = 12t + -12t + -10t2 + 10t2

Combine like terms: 12t + -12t = 0
-54 + -12t + 10t2 = 0 + -10t2 + 10t2
-54 + -12t + 10t2 = -10t2 + 10t2

Combine like terms: -10t2 + 10t2 = 0
-54 + -12t + 10t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + -6t + 5t2) = 0

Factor a trinomial.
2((-9 + -5t)(3 + -1t)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-9 + -5t)' equal to zero and attempt to solve: Simplifying -9 + -5t = 0 Solving -9 + -5t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -5t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5t = 0 + 9 -5t = 0 + 9 Combine like terms: 0 + 9 = 9 -5t = 9 Divide each side by '-5'. t = -1.8 Simplifying t = -1.8

Subproblem 2

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

Solution

t = {-1.8, 3}

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