4t^2+32t-240=0

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Solution for 4t^2+32t-240=0 equation: 


Simplifying
4t2 + 32t + -240 = 0

Reorder the terms:
-240 + 32t + 4t2 = 0

Solving
-240 + 32t + 4t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-60 + 8t + t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-60 + 8t + t2)' equal to zero and attempt to solve:

Simplifying
-60 + 8t + t2 = 0

Solving
-60 + 8t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 8t + 60 + t2 = 0 + 60

Reorder the terms:
-60 + 60 + 8t + t2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 8t + t2 = 0 + 60
8t + t2 = 0 + 60

Combine like terms: 0 + 60 = 60
8t + t2 = 60

The t term is 8t.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8t + 16 + t2 = 60 + 16

Reorder the terms:
16 + 8t + t2 = 60 + 16

Combine like terms: 60 + 16 = 76
16 + 8t + t2 = 76

Factor a perfect square on the left side:
(t + 4)(t + 4) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(t + 4) equal to 8.717797887 and -8.717797887.


Subproblem 1
t + 4 = 8.717797887

Simplifying
t + 4 = 8.717797887

Reorder the terms:
4 + t = 8.717797887

Solving
4 + t = 8.717797887

Solving for variable 't'.

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

Add '-4' to each side of the equation.
4 + -4 + t = 8.717797887 + -4

Combine like terms: 4 + -4 = 0
0 + t = 8.717797887 + -4
t = 8.717797887 + -4

Combine like terms: 8.717797887 + -4 = 4.717797887
t = 4.717797887

Simplifying
t = 4.717797887


Subproblem 2
t + 4 = -8.717797887

Simplifying
t + 4 = -8.717797887

Reorder the terms:
4 + t = -8.717797887

Solving
4 + t = -8.717797887

Solving for variable 't'.

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

Add '-4' to each side of the equation.
4 + -4 + t = -8.717797887 + -4

Combine like terms: 4 + -4 = 0
0 + t = -8.717797887 + -4
t = -8.717797887 + -4

Combine like terms: -8.717797887 + -4 = -12.717797887
t = -12.717797887

Simplifying
t = -12.717797887


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.717797887, -12.717797887}
Solution
t = {4.717797887, -12.717797887}

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