3t^2-18t+21=0

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Solution for 3t^2-18t+21=0 equation: 


Simplifying
3t2 + -18t + 21 = 0

Reorder the terms:
21 + -18t + 3t2 = 0

Solving
21 + -18t + 3t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + -6t + t2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + -6t + t2)' equal to zero and attempt to solve:

Simplifying
7 + -6t + t2 = 0

Solving
7 + -6t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -6t + -7 + t2 = 0 + -7

Reorder the terms:
7 + -7 + -6t + t2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6t + t2 = 0 + -7
-6t + t2 = 0 + -7

Combine like terms: 0 + -7 = -7
-6t + t2 = -7

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 = -7 + 9

Reorder the terms:
9 + -6t + t2 = -7 + 9

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

Factor a perfect square on the left side:
(t + -3)(t + -3) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(t + -3) equal to 1.414213562 and -1.414213562.


Subproblem 1
t + -3 = 1.414213562

Simplifying
t + -3 = 1.414213562

Reorder the terms:
-3 + t = 1.414213562

Solving
-3 + t = 1.414213562

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 = 1.414213562 + 3

Combine like terms: -3 + 3 = 0
0 + t = 1.414213562 + 3
t = 1.414213562 + 3

Combine like terms: 1.414213562 + 3 = 4.414213562
t = 4.414213562

Simplifying
t = 4.414213562


Subproblem 2
t + -3 = -1.414213562

Simplifying
t + -3 = -1.414213562

Reorder the terms:
-3 + t = -1.414213562

Solving
-3 + t = -1.414213562

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 = -1.414213562 + 3

Combine like terms: -3 + 3 = 0
0 + t = -1.414213562 + 3
t = -1.414213562 + 3

Combine like terms: -1.414213562 + 3 = 1.585786438
t = 1.585786438

Simplifying
t = 1.585786438


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.414213562, 1.585786438}
Solution
t = {4.414213562, 1.585786438}

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