-4(t-5)7t=8t-4

Solution for -4(t-5)7t=8t-4 equation:

Simplifying
-4(t + -5) * 7t = 8t + -4

Reorder the terms:
-4(-5 + t) * 7t = 8t + -4

Reorder the terms for easier multiplication:
-4 * 7t(-5 + t) = 8t + -4

Multiply -4 * 7
-28t(-5 + t) = 8t + -4
(-5 * -28t + t * -28t) = 8t + -4
(140t + -28t2) = 8t + -4

Reorder the terms:
140t + -28t2 = -4 + 8t

Solving
140t + -28t2 = -4 + 8t

Solving for variable 't'.

Reorder the terms:
4 + 140t + -8t + -28t2 = -4 + 8t + 4 + -8t

Combine like terms: 140t + -8t = 132t
4 + 132t + -28t2 = -4 + 8t + 4 + -8t

Reorder the terms:
4 + 132t + -28t2 = -4 + 4 + 8t + -8t

Combine like terms: -4 + 4 = 0
4 + 132t + -28t2 = 0 + 8t + -8t
4 + 132t + -28t2 = 8t + -8t

Combine like terms: 8t + -8t = 0
4 + 132t + -28t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 33t + -7t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + 33t + -7t2)' equal to zero and attempt to solve:

Simplifying
1 + 33t + -7t2 = 0

Solving
1 + 33t + -7t2 = 0

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

Divide each side by '-7'.
-0.1428571429 + -4.714285714t + t2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + -4.714285714t + 0.1428571429 + t2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + -4.714285714t + t2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + -4.714285714t + t2 = 0 + 0.1428571429
-4.714285714t + t2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
-4.714285714t + t2 = 0.1428571429

The t term is -4.714285714t.  Take half its coefficient (-2.357142857).
Square it (5.556122448) and add it to both sides.

Add '5.556122448' to each side of the equation.
-4.714285714t + 5.556122448 + t2 = 0.1428571429 + 5.556122448

Reorder the terms:
5.556122448 + -4.714285714t + t2 = 0.1428571429 + 5.556122448

Combine like terms: 0.1428571429 + 5.556122448 = 5.6989795909
5.556122448 + -4.714285714t + t2 = 5.6989795909

Factor a perfect square on the left side:
(t + -2.357142857)(t + -2.357142857) = 5.6989795909

Calculate the square root of the right side: 2.387253567

Break this problem into two subproblems by setting 
(t + -2.357142857) equal to 2.387253567 and -2.387253567.

Subproblem 1
t + -2.357142857 = 2.387253567

Simplifying
t + -2.357142857 = 2.387253567

Reorder the terms:
-2.357142857 + t = 2.387253567

Solving
-2.357142857 + t = 2.387253567

Solving for variable 't'.

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

Add '2.357142857' to each side of the equation.
-2.357142857 + 2.357142857 + t = 2.387253567 + 2.357142857

Combine like terms: -2.357142857 + 2.357142857 = 0.000000000
0.000000000 + t = 2.387253567 + 2.357142857
t = 2.387253567 + 2.357142857

Combine like terms: 2.387253567 + 2.357142857 = 4.744396424
t = 4.744396424

Simplifying
t = 4.744396424

Subproblem 2
t + -2.357142857 = -2.387253567

Simplifying
t + -2.357142857 = -2.387253567

Reorder the terms:
-2.357142857 + t = -2.387253567

Solving
-2.357142857 + t = -2.387253567

Solving for variable 't'.

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

Add '2.357142857' to each side of the equation.
-2.357142857 + 2.357142857 + t = -2.387253567 + 2.357142857

Combine like terms: -2.357142857 + 2.357142857 = 0.000000000
0.000000000 + t = -2.387253567 + 2.357142857
t = -2.387253567 + 2.357142857

Combine like terms: -2.387253567 + 2.357142857 = -0.03011071
t = -0.03011071

Simplifying
t = -0.03011071

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.744396424, -0.03011071}
Solution
t = {4.744396424, -0.03011071}