-5(t-4)t=5+1

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Solution for -5(t-4)t=5+1 equation:


Simplifying
-5(t + -4) * t = 5 + 1

Reorder the terms:
-5(-4 + t) * t = 5 + 1

Reorder the terms for easier multiplication:
-5t(-4 + t) = 5 + 1
(-4 * -5t + t * -5t) = 5 + 1
(20t + -5t2) = 5 + 1

Combine like terms: 5 + 1 = 6
20t + -5t2 = 6

Solving
20t + -5t2 = 6

Solving for variable 't'.

Reorder the terms:
-6 + 20t + -5t2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 20t + -5t2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
1.2 + -4t + t2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -4t + -1.2 + t2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -4t + t2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -4t + t2 = 0 + -1.2
-4t + t2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-4t + t2 = -1.2

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = -1.2 + 4

Reorder the terms:
4 + -4t + t2 = -1.2 + 4

Combine like terms: -1.2 + 4 = 2.8
4 + -4t + t2 = 2.8

Factor a perfect square on the left side:
(t + -2)(t + -2) = 2.8

Calculate the square root of the right side: 1.673320053

Break this problem into two subproblems by setting 
(t + -2) equal to 1.673320053 and -1.673320053.

Subproblem 1

t + -2 = 1.673320053 Simplifying t + -2 = 1.673320053 Reorder the terms: -2 + t = 1.673320053 Solving -2 + t = 1.673320053 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 1.673320053 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1.673320053 + 2 t = 1.673320053 + 2 Combine like terms: 1.673320053 + 2 = 3.673320053 t = 3.673320053 Simplifying t = 3.673320053

Subproblem 2

t + -2 = -1.673320053 Simplifying t + -2 = -1.673320053 Reorder the terms: -2 + t = -1.673320053 Solving -2 + t = -1.673320053 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -1.673320053 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1.673320053 + 2 t = -1.673320053 + 2 Combine like terms: -1.673320053 + 2 = 0.326679947 t = 0.326679947 Simplifying t = 0.326679947

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.673320053, 0.326679947}

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