4-2(5t+5)4(2+t)=13

Solution for 4-2(5t+5)4(2+t)=13 equation:

Simplifying
4 + -2(5t + 5) * 4(2 + t) = 13

Reorder the terms:
4 + -2(5 + 5t) * 4(2 + t) = 13

Reorder the terms for easier multiplication:
4 + -2 * 4(5 + 5t)(2 + t) = 13

Multiply -2 * 4
4 + -8(5 + 5t)(2 + t) = 13

Multiply (5 + 5t) * (2 + t)
4 + -8(5(2 + t) + 5t * (2 + t)) = 13
4 + -8((2 * 5 + t * 5) + 5t * (2 + t)) = 13
4 + -8((10 + 5t) + 5t * (2 + t)) = 13
4 + -8(10 + 5t + (2 * 5t + t * 5t)) = 13
4 + -8(10 + 5t + (10t + 5t2)) = 13

Combine like terms: 5t + 10t = 15t
4 + -8(10 + 15t + 5t2) = 13
4 + (10 * -8 + 15t * -8 + 5t2 * -8) = 13
4 + (-80 + -120t + -40t2) = 13

Combine like terms: 4 + -80 = -76
-76 + -120t + -40t2 = 13

Solving
-76 + -120t + -40t2 = 13

Solving for variable 't'.

Reorder the terms:
-76 + -13 + -120t + -40t2 = 13 + -13

Combine like terms: -76 + -13 = -89
-89 + -120t + -40t2 = 13 + -13

Combine like terms: 13 + -13 = 0
-89 + -120t + -40t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(89 + 120t + 40t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(89 + 120t + 40t2)' equal to zero and attempt to solve:

Simplifying
89 + 120t + 40t2 = 0

Solving
89 + 120t + 40t2 = 0

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

Divide each side by '40'.
2.225 + 3t + t2 = 0.0

Move the constant term to the right:

Add '-2.225' to each side of the equation.
2.225 + 3t + -2.225 + t2 = 0.0 + -2.225

Reorder the terms:
2.225 + -2.225 + 3t + t2 = 0.0 + -2.225

Combine like terms: 2.225 + -2.225 = 0.000
0.000 + 3t + t2 = 0.0 + -2.225
3t + t2 = 0.0 + -2.225

Combine like terms: 0.0 + -2.225 = -2.225
3t + t2 = -2.225

The t term is 3t.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3t + 2.25 + t2 = -2.225 + 2.25

Reorder the terms:
2.25 + 3t + t2 = -2.225 + 2.25

Combine like terms: -2.225 + 2.25 = 0.025
2.25 + 3t + t2 = 0.025

Factor a perfect square on the left side:
(t + 1.5)(t + 1.5) = 0.025

Calculate the square root of the right side: 0.158113883

Break this problem into two subproblems by setting 
(t + 1.5) equal to 0.158113883 and -0.158113883.

Subproblem 1
t + 1.5 = 0.158113883

Simplifying
t + 1.5 = 0.158113883

Reorder the terms:
1.5 + t = 0.158113883

Solving
1.5 + t = 0.158113883

Solving for variable 't'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + t = 0.158113883 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = 0.158113883 + -1.5
t = 0.158113883 + -1.5

Combine like terms: 0.158113883 + -1.5 = -1.341886117
t = -1.341886117

Simplifying
t = -1.341886117

Subproblem 2
t + 1.5 = -0.158113883

Simplifying
t + 1.5 = -0.158113883

Reorder the terms:
1.5 + t = -0.158113883

Solving
1.5 + t = -0.158113883

Solving for variable 't'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + t = -0.158113883 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = -0.158113883 + -1.5
t = -0.158113883 + -1.5

Combine like terms: -0.158113883 + -1.5 = -1.658113883
t = -1.658113883

Simplifying
t = -1.658113883

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-1.341886117, -1.658113883}
Solution
t = {-1.341886117, -1.658113883}