4t^2-28t-180=0

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Solution for 4t^2-28t-180=0 equation: 


Simplifying
4t2 + -28t + -180 = 0

Reorder the terms:
-180 + -28t + 4t2 = 0

Solving
-180 + -28t + 4t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + -7t + t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-45 + -7t + t2)' equal to zero and attempt to solve:

Simplifying
-45 + -7t + t2 = 0

Solving
-45 + -7t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -7t + 45 + t2 = 0 + 45

Reorder the terms:
-45 + 45 + -7t + t2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -7t + t2 = 0 + 45
-7t + t2 = 0 + 45

Combine like terms: 0 + 45 = 45
-7t + t2 = 45

The t term is -7t.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7t + 12.25 + t2 = 45 + 12.25

Reorder the terms:
12.25 + -7t + t2 = 45 + 12.25

Combine like terms: 45 + 12.25 = 57.25
12.25 + -7t + t2 = 57.25

Factor a perfect square on the left side:
(t + -3.5)(t + -3.5) = 57.25

Calculate the square root of the right side: 7.566372975

Break this problem into two subproblems by setting 
(t + -3.5) equal to 7.566372975 and -7.566372975.


Subproblem 1
t + -3.5 = 7.566372975

Simplifying
t + -3.5 = 7.566372975

Reorder the terms:
-3.5 + t = 7.566372975

Solving
-3.5 + t = 7.566372975

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = 7.566372975 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = 7.566372975 + 3.5
t = 7.566372975 + 3.5

Combine like terms: 7.566372975 + 3.5 = 11.066372975
t = 11.066372975

Simplifying
t = 11.066372975


Subproblem 2
t + -3.5 = -7.566372975

Simplifying
t + -3.5 = -7.566372975

Reorder the terms:
-3.5 + t = -7.566372975

Solving
-3.5 + t = -7.566372975

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = -7.566372975 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = -7.566372975 + 3.5
t = -7.566372975 + 3.5

Combine like terms: -7.566372975 + 3.5 = -4.066372975
t = -4.066372975

Simplifying
t = -4.066372975


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {11.066372975, -4.066372975}
Solution
t = {11.066372975, -4.066372975}

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