-7=3(t-5)t

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Solution for -7=3(t-5)t equation: 


Simplifying
-7 = 3(t + -5) * t

Reorder the terms:
-7 = 3(-5 + t) * t

Reorder the terms for easier multiplication:
-7 = 3t(-5 + t)
-7 = (-5 * 3t + t * 3t)
-7 = (-15t + 3t2)

Solving
-7 = -15t + 3t2

Solving for variable 't'.

Reorder the terms:
-7 + 15t + -3t2 = -15t + 15t + 3t2 + -3t2

Combine like terms: -15t + 15t = 0
-7 + 15t + -3t2 = 0 + 3t2 + -3t2
-7 + 15t + -3t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
-7 + 15t + -3t2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
2.333333333 + -5t + t2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -5t + -2.333333333 + t2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -5t + t2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -5t + t2 = 0 + -2.333333333
-5t + t2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-5t + t2 = -2.333333333

The t term is -5t.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5t + 6.25 + t2 = -2.333333333 + 6.25

Reorder the terms:
6.25 + -5t + t2 = -2.333333333 + 6.25

Combine like terms: -2.333333333 + 6.25 = 3.916666667
6.25 + -5t + t2 = 3.916666667

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 3.916666667

Calculate the square root of the right side: 1.979057015

Break this problem into two subproblems by setting 
(t + -2.5) equal to 1.979057015 and -1.979057015.


Subproblem 1
t + -2.5 = 1.979057015

Simplifying
t + -2.5 = 1.979057015

Reorder the terms:
-2.5 + t = 1.979057015

Solving
-2.5 + t = 1.979057015

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = 1.979057015 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 1.979057015 + 2.5
t = 1.979057015 + 2.5

Combine like terms: 1.979057015 + 2.5 = 4.479057015
t = 4.479057015

Simplifying
t = 4.479057015


Subproblem 2
t + -2.5 = -1.979057015

Simplifying
t + -2.5 = -1.979057015

Reorder the terms:
-2.5 + t = -1.979057015

Solving
-2.5 + t = -1.979057015

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = -1.979057015 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -1.979057015 + 2.5
t = -1.979057015 + 2.5

Combine like terms: -1.979057015 + 2.5 = 0.520942985
t = 0.520942985

Simplifying
t = 0.520942985


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.479057015, 0.520942985}

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