47t(t-6)=180

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Solution for 47t(t-6)=180 equation:


Simplifying
47t(t + -6) = 180

Reorder the terms:
47t(-6 + t) = 180
(-6 * 47t + t * 47t) = 180
(-282t + 47t2) = 180

Solving
-282t + 47t2 = 180

Solving for variable 't'.

Reorder the terms:
-180 + -282t + 47t2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -282t + 47t2 = 0

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

Divide each side by '47'.
-3.829787234 + -6t + t2 = 0

Move the constant term to the right:

Add '3.829787234' to each side of the equation.
-3.829787234 + -6t + 3.829787234 + t2 = 0 + 3.829787234

Reorder the terms:
-3.829787234 + 3.829787234 + -6t + t2 = 0 + 3.829787234

Combine like terms: -3.829787234 + 3.829787234 = 0.000000000
0.000000000 + -6t + t2 = 0 + 3.829787234
-6t + t2 = 0 + 3.829787234

Combine like terms: 0 + 3.829787234 = 3.829787234
-6t + t2 = 3.829787234

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = 3.829787234 + 9

Reorder the terms:
9 + -6t + t2 = 3.829787234 + 9

Combine like terms: 3.829787234 + 9 = 12.829787234
9 + -6t + t2 = 12.829787234

Factor a perfect square on the left side:
(t + -3)(t + -3) = 12.829787234

Calculate the square root of the right side: 3.581869237

Break this problem into two subproblems by setting 
(t + -3) equal to 3.581869237 and -3.581869237.

Subproblem 1

t + -3 = 3.581869237 Simplifying t + -3 = 3.581869237 Reorder the terms: -3 + t = 3.581869237 Solving -3 + t = 3.581869237 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 3.581869237 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.581869237 + 3 t = 3.581869237 + 3 Combine like terms: 3.581869237 + 3 = 6.581869237 t = 6.581869237 Simplifying t = 6.581869237

Subproblem 2

t + -3 = -3.581869237 Simplifying t + -3 = -3.581869237 Reorder the terms: -3 + t = -3.581869237 Solving -3 + t = -3.581869237 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -3.581869237 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.581869237 + 3 t = -3.581869237 + 3 Combine like terms: -3.581869237 + 3 = -0.581869237 t = -0.581869237 Simplifying t = -0.581869237

Solution

The solution to the problem is based on the solutions from the subproblems. t = {6.581869237, -0.581869237}

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