-4(t-7)(t+2)=11

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Solution for -4(t-7)(t+2)=11 equation: 


Simplifying
-4(t + -7)(t + 2) = 11

Reorder the terms:
-4(-7 + t)(t + 2) = 11

Reorder the terms:
-4(-7 + t)(2 + t) = 11

Multiply (-7 + t) * (2 + t)
-4(-7(2 + t) + t(2 + t)) = 11
-4((2 * -7 + t * -7) + t(2 + t)) = 11
-4((-14 + -7t) + t(2 + t)) = 11
-4(-14 + -7t + (2 * t + t * t)) = 11
-4(-14 + -7t + (2t + t2)) = 11

Combine like terms: -7t + 2t = -5t
-4(-14 + -5t + t2) = 11
(-14 * -4 + -5t * -4 + t2 * -4) = 11
(56 + 20t + -4t2) = 11

Solving
56 + 20t + -4t2 = 11

Solving for variable 't'.

Reorder the terms:
56 + -11 + 20t + -4t2 = 11 + -11

Combine like terms: 56 + -11 = 45
45 + 20t + -4t2 = 11 + -11

Combine like terms: 11 + -11 = 0
45 + 20t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-11.25 + -5t + t2 = 0

Move the constant term to the right:

Add '11.25' to each side of the equation.
-11.25 + -5t + 11.25 + t2 = 0 + 11.25

Reorder the terms:
-11.25 + 11.25 + -5t + t2 = 0 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + -5t + t2 = 0 + 11.25
-5t + t2 = 0 + 11.25

Combine like terms: 0 + 11.25 = 11.25
-5t + t2 = 11.25

The t term is -5t.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5t + 6.25 + t2 = 11.25 + 6.25

Reorder the terms:
6.25 + -5t + t2 = 11.25 + 6.25

Combine like terms: 11.25 + 6.25 = 17.5
6.25 + -5t + t2 = 17.5

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 17.5

Calculate the square root of the right side: 4.183300133

Break this problem into two subproblems by setting 
(t + -2.5) equal to 4.183300133 and -4.183300133.


Subproblem 1
t + -2.5 = 4.183300133

Simplifying
t + -2.5 = 4.183300133

Reorder the terms:
-2.5 + t = 4.183300133

Solving
-2.5 + t = 4.183300133

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = 4.183300133 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 4.183300133 + 2.5
t = 4.183300133 + 2.5

Combine like terms: 4.183300133 + 2.5 = 6.683300133
t = 6.683300133

Simplifying
t = 6.683300133


Subproblem 2
t + -2.5 = -4.183300133

Simplifying
t + -2.5 = -4.183300133

Reorder the terms:
-2.5 + t = -4.183300133

Solving
-2.5 + t = -4.183300133

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = -4.183300133 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -4.183300133 + 2.5
t = -4.183300133 + 2.5

Combine like terms: -4.183300133 + 2.5 = -1.683300133
t = -1.683300133

Simplifying
t = -1.683300133


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.683300133, -1.683300133}

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