7=-16t^2+24t+1

Solution for 7=-16t^2+24t+1 equation:

Simplifying
7 = -16t2 + 24t + 1

Reorder the terms:
7 = 1 + 24t + -16t2

Solving
7 = 1 + 24t + -16t2

Solving for variable 't'.

Combine like terms: 7 + -1 = 6
6 + -24t + 16t2 = 1 + 24t + -16t2 + -1 + -24t + 16t2

Reorder the terms:
6 + -24t + 16t2 = 1 + -1 + 24t + -24t + -16t2 + 16t2

Combine like terms: 1 + -1 = 0
6 + -24t + 16t2 = 0 + 24t + -24t + -16t2 + 16t2
6 + -24t + 16t2 = 24t + -24t + -16t2 + 16t2

Combine like terms: 24t + -24t = 0
6 + -24t + 16t2 = 0 + -16t2 + 16t2
6 + -24t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
6 + -24t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -12t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -12t + 8t2)' equal to zero and attempt to solve:

Simplifying
3 + -12t + 8t2 = 0

Solving
3 + -12t + 8t2 = 0

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

Divide each side by '8'.
0.375 + -1.5t + t2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + -1.5t + -0.375 + t2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + -1.5t + t2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + -1.5t + t2 = 0 + -0.375
-1.5t + t2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
-1.5t + t2 = -0.375

The t term is -1.5t.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5t + 0.5625 + t2 = -0.375 + 0.5625

Reorder the terms:
0.5625 + -1.5t + t2 = -0.375 + 0.5625

Combine like terms: -0.375 + 0.5625 = 0.1875
0.5625 + -1.5t + t2 = 0.1875

Factor a perfect square on the left side:
(t + -0.75)(t + -0.75) = 0.1875

Calculate the square root of the right side: 0.433012702

Break this problem into two subproblems by setting 
(t + -0.75) equal to 0.433012702 and -0.433012702.

Subproblem 1
t + -0.75 = 0.433012702

Simplifying
t + -0.75 = 0.433012702

Reorder the terms:
-0.75 + t = 0.433012702

Solving
-0.75 + t = 0.433012702

Solving for variable 't'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + t = 0.433012702 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = 0.433012702 + 0.75
t = 0.433012702 + 0.75

Combine like terms: 0.433012702 + 0.75 = 1.183012702
t = 1.183012702

Simplifying
t = 1.183012702

Subproblem 2
t + -0.75 = -0.433012702

Simplifying
t + -0.75 = -0.433012702

Reorder the terms:
-0.75 + t = -0.433012702

Solving
-0.75 + t = -0.433012702

Solving for variable 't'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + t = -0.433012702 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + t = -0.433012702 + 0.75
t = -0.433012702 + 0.75

Combine like terms: -0.433012702 + 0.75 = 0.316987298
t = 0.316987298

Simplifying
t = 0.316987298

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.183012702, 0.316987298}
Solution
t = {1.183012702, 0.316987298}