-5=3(t-8)2t

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Solution for -5=3(t-8)2t equation:


Simplifying
-5 = 3(t + -8) * 2t

Reorder the terms:
-5 = 3(-8 + t) * 2t

Reorder the terms for easier multiplication:
-5 = 3 * 2t(-8 + t)

Multiply 3 * 2
-5 = 6t(-8 + t)
-5 = (-8 * 6t + t * 6t)
-5 = (-48t + 6t2)

Solving
-5 = -48t + 6t2

Solving for variable 't'.

Reorder the terms:
-5 + 48t + -6t2 = -48t + 48t + 6t2 + -6t2

Combine like terms: -48t + 48t = 0
-5 + 48t + -6t2 = 0 + 6t2 + -6t2
-5 + 48t + -6t2 = 6t2 + -6t2

Combine like terms: 6t2 + -6t2 = 0
-5 + 48t + -6t2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
0.8333333333 + -8t + t2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + -8t + -0.8333333333 + t2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + -8t + t2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + -8t + t2 = 0 + -0.8333333333
-8t + t2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
-8t + t2 = -0.8333333333

The t term is -8t.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8t + 16 + t2 = -0.8333333333 + 16

Reorder the terms:
16 + -8t + t2 = -0.8333333333 + 16

Combine like terms: -0.8333333333 + 16 = 15.1666666667
16 + -8t + t2 = 15.1666666667

Factor a perfect square on the left side:
(t + -4)(t + -4) = 15.1666666667

Calculate the square root of the right side: 3.894440482

Break this problem into two subproblems by setting 
(t + -4) equal to 3.894440482 and -3.894440482.

Subproblem 1

t + -4 = 3.894440482 Simplifying t + -4 = 3.894440482 Reorder the terms: -4 + t = 3.894440482 Solving -4 + t = 3.894440482 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 3.894440482 + 4 Combine like terms: -4 + 4 = 0 0 + t = 3.894440482 + 4 t = 3.894440482 + 4 Combine like terms: 3.894440482 + 4 = 7.894440482 t = 7.894440482 Simplifying t = 7.894440482

Subproblem 2

t + -4 = -3.894440482 Simplifying t + -4 = -3.894440482 Reorder the terms: -4 + t = -3.894440482 Solving -4 + t = -3.894440482 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -3.894440482 + 4 Combine like terms: -4 + 4 = 0 0 + t = -3.894440482 + 4 t = -3.894440482 + 4 Combine like terms: -3.894440482 + 4 = 0.105559518 t = 0.105559518 Simplifying t = 0.105559518

Solution

The solution to the problem is based on the solutions from the subproblems. t = {7.894440482, 0.105559518}

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