-3t^2+42t+21=0

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Solution for -3t^2+42t+21=0 equation: 


Simplifying
-3t2 + 42t + 21 = 0

Reorder the terms:
21 + 42t + -3t2 = 0

Solving
21 + 42t + -3t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + 14t + -1t2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + 14t + -1t2)' equal to zero and attempt to solve:

Simplifying
7 + 14t + -1t2 = 0

Solving
7 + 14t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-7 + -14t + t2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -14t + 7 + t2 = 0 + 7

Reorder the terms:
-7 + 7 + -14t + t2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -14t + t2 = 0 + 7
-14t + t2 = 0 + 7

Combine like terms: 0 + 7 = 7
-14t + t2 = 7

The t term is -14t.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14t + 49 + t2 = 7 + 49

Reorder the terms:
49 + -14t + t2 = 7 + 49

Combine like terms: 7 + 49 = 56
49 + -14t + t2 = 56

Factor a perfect square on the left side:
(t + -7)(t + -7) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(t + -7) equal to 7.483314774 and -7.483314774.


Subproblem 1
t + -7 = 7.483314774

Simplifying
t + -7 = 7.483314774

Reorder the terms:
-7 + t = 7.483314774

Solving
-7 + t = 7.483314774

Solving for variable 't'.

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

Add '7' to each side of the equation.
-7 + 7 + t = 7.483314774 + 7

Combine like terms: -7 + 7 = 0
0 + t = 7.483314774 + 7
t = 7.483314774 + 7

Combine like terms: 7.483314774 + 7 = 14.483314774
t = 14.483314774

Simplifying
t = 14.483314774


Subproblem 2
t + -7 = -7.483314774

Simplifying
t + -7 = -7.483314774

Reorder the terms:
-7 + t = -7.483314774

Solving
-7 + t = -7.483314774

Solving for variable 't'.

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

Add '7' to each side of the equation.
-7 + 7 + t = -7.483314774 + 7

Combine like terms: -7 + 7 = 0
0 + t = -7.483314774 + 7
t = -7.483314774 + 7

Combine like terms: -7.483314774 + 7 = -0.483314774
t = -0.483314774

Simplifying
t = -0.483314774


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {14.483314774, -0.483314774}
Solution
t = {14.483314774, -0.483314774}

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