40=-16t^2+42t+6

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Solution for 40=-16t^2+42t+6 equation: 


Simplifying
40 = -16t2 + 42t + 6

Reorder the terms:
40 = 6 + 42t + -16t2

Solving
40 = 6 + 42t + -16t2

Solving for variable 't'.

Combine like terms: 40 + -6 = 34
34 + -42t + 16t2 = 6 + 42t + -16t2 + -6 + -42t + 16t2

Reorder the terms:
34 + -42t + 16t2 = 6 + -6 + 42t + -42t + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
34 + -42t + 16t2 = 0 + 42t + -42t + -16t2 + 16t2
34 + -42t + 16t2 = 42t + -42t + -16t2 + 16t2

Combine like terms: 42t + -42t = 0
34 + -42t + 16t2 = 0 + -16t2 + 16t2
34 + -42t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
34 + -42t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + -21t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(17 + -21t + 8t2)' equal to zero and attempt to solve:

Simplifying
17 + -21t + 8t2 = 0

Solving
17 + -21t + 8t2 = 0

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

Divide each side by '8'.
2.125 + -2.625t + t2 = 0

Move the constant term to the right:

Add '-2.125' to each side of the equation.
2.125 + -2.625t + -2.125 + t2 = 0 + -2.125

Reorder the terms:
2.125 + -2.125 + -2.625t + t2 = 0 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + -2.625t + t2 = 0 + -2.125
-2.625t + t2 = 0 + -2.125

Combine like terms: 0 + -2.125 = -2.125
-2.625t + t2 = -2.125

The t term is -2.625t.  Take half its coefficient (-1.3125).
Square it (1.72265625) and add it to both sides.

Add '1.72265625' to each side of the equation.
-2.625t + 1.72265625 + t2 = -2.125 + 1.72265625

Reorder the terms:
1.72265625 + -2.625t + t2 = -2.125 + 1.72265625

Combine like terms: -2.125 + 1.72265625 = -0.40234375
1.72265625 + -2.625t + t2 = -0.40234375

Factor a perfect square on the left side:
(t + -1.3125)(t + -1.3125) = -0.40234375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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