7(t-5)7t=7(2t+4)-11

Solution for 7(t-5)7t=7(2t+4)-11 equation:

Simplifying
7(t + -5) * 7t = 7(2t + 4) + -11

Reorder the terms:
7(-5 + t) * 7t = 7(2t + 4) + -11

Reorder the terms for easier multiplication:
7 * 7t(-5 + t) = 7(2t + 4) + -11

Multiply 7 * 7
49t(-5 + t) = 7(2t + 4) + -11
(-5 * 49t + t * 49t) = 7(2t + 4) + -11
(-245t + 49t2) = 7(2t + 4) + -11

Reorder the terms:
-245t + 49t2 = 7(4 + 2t) + -11
-245t + 49t2 = (4 * 7 + 2t * 7) + -11
-245t + 49t2 = (28 + 14t) + -11

Reorder the terms:
-245t + 49t2 = 28 + -11 + 14t

Combine like terms: 28 + -11 = 17
-245t + 49t2 = 17 + 14t

Solving
-245t + 49t2 = 17 + 14t

Solving for variable 't'.

Reorder the terms:
-17 + -245t + -14t + 49t2 = 17 + 14t + -17 + -14t

Combine like terms: -245t + -14t = -259t
-17 + -259t + 49t2 = 17 + 14t + -17 + -14t

Reorder the terms:
-17 + -259t + 49t2 = 17 + -17 + 14t + -14t

Combine like terms: 17 + -17 = 0
-17 + -259t + 49t2 = 0 + 14t + -14t
-17 + -259t + 49t2 = 14t + -14t

Combine like terms: 14t + -14t = 0
-17 + -259t + 49t2 = 0

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

Divide each side by '49'.
-0.3469387755 + -5.285714286t + t2 = 0

Move the constant term to the right:

Add '0.3469387755' to each side of the equation.
-0.3469387755 + -5.285714286t + 0.3469387755 + t2 = 0 + 0.3469387755

Reorder the terms:
-0.3469387755 + 0.3469387755 + -5.285714286t + t2 = 0 + 0.3469387755

Combine like terms: -0.3469387755 + 0.3469387755 = 0.0000000000
0.0000000000 + -5.285714286t + t2 = 0 + 0.3469387755
-5.285714286t + t2 = 0 + 0.3469387755

Combine like terms: 0 + 0.3469387755 = 0.3469387755
-5.285714286t + t2 = 0.3469387755

The t term is -5.285714286t.  Take half its coefficient (-2.642857143).
Square it (6.984693878) and add it to both sides.

Add '6.984693878' to each side of the equation.
-5.285714286t + 6.984693878 + t2 = 0.3469387755 + 6.984693878

Reorder the terms:
6.984693878 + -5.285714286t + t2 = 0.3469387755 + 6.984693878

Combine like terms: 0.3469387755 + 6.984693878 = 7.3316326535
6.984693878 + -5.285714286t + t2 = 7.3316326535

Factor a perfect square on the left side:
(t + -2.642857143)(t + -2.642857143) = 7.3316326535

Calculate the square root of the right side: 2.707698775

Break this problem into two subproblems by setting 
(t + -2.642857143) equal to 2.707698775 and -2.707698775.

Subproblem 1
t + -2.642857143 = 2.707698775

Simplifying
t + -2.642857143 = 2.707698775

Reorder the terms:
-2.642857143 + t = 2.707698775

Solving
-2.642857143 + t = 2.707698775

Solving for variable 't'.

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

Add '2.642857143' to each side of the equation.
-2.642857143 + 2.642857143 + t = 2.707698775 + 2.642857143

Combine like terms: -2.642857143 + 2.642857143 = 0.000000000
0.000000000 + t = 2.707698775 + 2.642857143
t = 2.707698775 + 2.642857143

Combine like terms: 2.707698775 + 2.642857143 = 5.350555918
t = 5.350555918

Simplifying
t = 5.350555918

Subproblem 2
t + -2.642857143 = -2.707698775

Simplifying
t + -2.642857143 = -2.707698775

Reorder the terms:
-2.642857143 + t = -2.707698775

Solving
-2.642857143 + t = -2.707698775

Solving for variable 't'.

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

Add '2.642857143' to each side of the equation.
-2.642857143 + 2.642857143 + t = -2.707698775 + 2.642857143

Combine like terms: -2.642857143 + 2.642857143 = 0.000000000
0.000000000 + t = -2.707698775 + 2.642857143
t = -2.707698775 + 2.642857143

Combine like terms: -2.707698775 + 2.642857143 = -0.064841632
t = -0.064841632

Simplifying
t = -0.064841632

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.350555918, -0.064841632}