12=2+30t-5t^2

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Solution for 12=2+30t-5t^2 equation: 


Simplifying
12 = 2 + 30t + -5t2

Solving
12 = 2 + 30t + -5t2

Solving for variable 't'.

Combine like terms: 12 + -2 = 10
10 + -30t + 5t2 = 2 + 30t + -5t2 + -2 + -30t + 5t2

Reorder the terms:
10 + -30t + 5t2 = 2 + -2 + 30t + -30t + -5t2 + 5t2

Combine like terms: 2 + -2 = 0
10 + -30t + 5t2 = 0 + 30t + -30t + -5t2 + 5t2
10 + -30t + 5t2 = 30t + -30t + -5t2 + 5t2

Combine like terms: 30t + -30t = 0
10 + -30t + 5t2 = 0 + -5t2 + 5t2
10 + -30t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
10 + -30t + 5t2 = 0

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

Ignore the factor 5.

Subproblem 1
Set the factor '(2 + -6t + t2)' equal to zero and attempt to solve:

Simplifying
2 + -6t + t2 = 0

Solving
2 + -6t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -6t + -2 + t2 = 0 + -2

Reorder the terms:
2 + -2 + -6t + t2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -6t + t2 = 0 + -2
-6t + t2 = 0 + -2

Combine like terms: 0 + -2 = -2
-6t + t2 = -2

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = -2 + 9

Reorder the terms:
9 + -6t + t2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + -6t + t2 = 7

Factor a perfect square on the left side:
(t + -3)(t + -3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(t + -3) equal to 2.645751311 and -2.645751311.


Subproblem 1
t + -3 = 2.645751311

Simplifying
t + -3 = 2.645751311

Reorder the terms:
-3 + t = 2.645751311

Solving
-3 + t = 2.645751311

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + t = 2.645751311 + 3

Combine like terms: -3 + 3 = 0
0 + t = 2.645751311 + 3
t = 2.645751311 + 3

Combine like terms: 2.645751311 + 3 = 5.645751311
t = 5.645751311

Simplifying
t = 5.645751311


Subproblem 2
t + -3 = -2.645751311

Simplifying
t + -3 = -2.645751311

Reorder the terms:
-3 + t = -2.645751311

Solving
-3 + t = -2.645751311

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + t = -2.645751311 + 3

Combine like terms: -3 + 3 = 0
0 + t = -2.645751311 + 3
t = -2.645751311 + 3

Combine like terms: -2.645751311 + 3 = 0.354248689
t = 0.354248689

Simplifying
t = 0.354248689


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.645751311, 0.354248689}
Solution
t = {5.645751311, 0.354248689}

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