7(t^2+5t-9)+t=(7t-2)+13

Solution for 7(t^2+5t-9)+t=(7t-2)+13 equation:

Simplifying
7(t2 + 5t + -9) + t = (7t + -2) + 13

Reorder the terms:
7(-9 + 5t + t2) + t = (7t + -2) + 13
(-9 * 7 + 5t * 7 + t2 * 7) + t = (7t + -2) + 13
(-63 + 35t + 7t2) + t = (7t + -2) + 13

Reorder the terms:
-63 + 35t + t + 7t2 = (7t + -2) + 13

Combine like terms: 35t + t = 36t
-63 + 36t + 7t2 = (7t + -2) + 13

Reorder the terms:
-63 + 36t + 7t2 = (-2 + 7t) + 13

Remove parenthesis around (-2 + 7t)
-63 + 36t + 7t2 = -2 + 7t + 13

Reorder the terms:
-63 + 36t + 7t2 = -2 + 13 + 7t

Combine like terms: -2 + 13 = 11
-63 + 36t + 7t2 = 11 + 7t

Solving
-63 + 36t + 7t2 = 11 + 7t

Solving for variable 't'.

Reorder the terms:
-63 + -11 + 36t + -7t + 7t2 = 11 + 7t + -11 + -7t

Combine like terms: -63 + -11 = -74
-74 + 36t + -7t + 7t2 = 11 + 7t + -11 + -7t

Combine like terms: 36t + -7t = 29t
-74 + 29t + 7t2 = 11 + 7t + -11 + -7t

Reorder the terms:
-74 + 29t + 7t2 = 11 + -11 + 7t + -7t

Combine like terms: 11 + -11 = 0
-74 + 29t + 7t2 = 0 + 7t + -7t
-74 + 29t + 7t2 = 7t + -7t

Combine like terms: 7t + -7t = 0
-74 + 29t + 7t2 = 0

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

Divide each side by '7'.
-10.57142857 + 4.142857143t + t2 = 0

Move the constant term to the right:

Add '10.57142857' to each side of the equation.
-10.57142857 + 4.142857143t + 10.57142857 + t2 = 0 + 10.57142857

Reorder the terms:
-10.57142857 + 10.57142857 + 4.142857143t + t2 = 0 + 10.57142857

Combine like terms: -10.57142857 + 10.57142857 = 0.00000000
0.00000000 + 4.142857143t + t2 = 0 + 10.57142857
4.142857143t + t2 = 0 + 10.57142857

Combine like terms: 0 + 10.57142857 = 10.57142857
4.142857143t + t2 = 10.57142857

The t term is 4.142857143t.  Take half its coefficient (2.071428572).
Square it (4.290816329) and add it to both sides.

Add '4.290816329' to each side of the equation.
4.142857143t + 4.290816329 + t2 = 10.57142857 + 4.290816329

Reorder the terms:
4.290816329 + 4.142857143t + t2 = 10.57142857 + 4.290816329

Combine like terms: 10.57142857 + 4.290816329 = 14.862244899
4.290816329 + 4.142857143t + t2 = 14.862244899

Factor a perfect square on the left side:
(t + 2.071428572)(t + 2.071428572) = 14.862244899

Calculate the square root of the right side: 3.85515822

Break this problem into two subproblems by setting 
(t + 2.071428572) equal to 3.85515822 and -3.85515822.

Subproblem 1
t + 2.071428572 = 3.85515822

Simplifying
t + 2.071428572 = 3.85515822

Reorder the terms:
2.071428572 + t = 3.85515822

Solving
2.071428572 + t = 3.85515822

Solving for variable 't'.

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

Add '-2.071428572' to each side of the equation.
2.071428572 + -2.071428572 + t = 3.85515822 + -2.071428572

Combine like terms: 2.071428572 + -2.071428572 = 0.000000000
0.000000000 + t = 3.85515822 + -2.071428572
t = 3.85515822 + -2.071428572

Combine like terms: 3.85515822 + -2.071428572 = 1.783729648
t = 1.783729648

Simplifying
t = 1.783729648

Subproblem 2
t + 2.071428572 = -3.85515822

Simplifying
t + 2.071428572 = -3.85515822

Reorder the terms:
2.071428572 + t = -3.85515822

Solving
2.071428572 + t = -3.85515822

Solving for variable 't'.

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

Add '-2.071428572' to each side of the equation.
2.071428572 + -2.071428572 + t = -3.85515822 + -2.071428572

Combine like terms: 2.071428572 + -2.071428572 = 0.000000000
0.000000000 + t = -3.85515822 + -2.071428572
t = -3.85515822 + -2.071428572

Combine like terms: -3.85515822 + -2.071428572 = -5.926586792
t = -5.926586792

Simplifying
t = -5.926586792

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.783729648, -5.926586792}