t=(-2+t)(t-7)

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Solution for t=(-2+t)(t-7) equation:


Simplifying
t = (-2 + t)(t + -7)

Reorder the terms:
t = (-2 + t)(-7 + t)

Multiply (-2 + t) * (-7 + t)
t = (-2(-7 + t) + t(-7 + t))
t = ((-7 * -2 + t * -2) + t(-7 + t))
t = ((14 + -2t) + t(-7 + t))
t = (14 + -2t + (-7 * t + t * t))
t = (14 + -2t + (-7t + t2))

Combine like terms: -2t + -7t = -9t
t = (14 + -9t + t2)

Solving
t = 14 + -9t + t2

Solving for variable 't'.

Reorder the terms:
-14 + t + 9t + -1t2 = 14 + -9t + t2 + -14 + 9t + -1t2

Combine like terms: t + 9t = 10t
-14 + 10t + -1t2 = 14 + -9t + t2 + -14 + 9t + -1t2

Reorder the terms:
-14 + 10t + -1t2 = 14 + -14 + -9t + 9t + t2 + -1t2

Combine like terms: 14 + -14 = 0
-14 + 10t + -1t2 = 0 + -9t + 9t + t2 + -1t2
-14 + 10t + -1t2 = -9t + 9t + t2 + -1t2

Combine like terms: -9t + 9t = 0
-14 + 10t + -1t2 = 0 + t2 + -1t2
-14 + 10t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-14 + 10t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
14 + -10t + t2 = 0

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -10t + -14 + t2 = 0 + -14

Reorder the terms:
14 + -14 + -10t + t2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -10t + t2 = 0 + -14
-10t + t2 = 0 + -14

Combine like terms: 0 + -14 = -14
-10t + t2 = -14

The t term is -10t.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10t + 25 + t2 = -14 + 25

Reorder the terms:
25 + -10t + t2 = -14 + 25

Combine like terms: -14 + 25 = 11
25 + -10t + t2 = 11

Factor a perfect square on the left side:
(t + -5)(t + -5) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(t + -5) equal to 3.31662479 and -3.31662479.

Subproblem 1

t + -5 = 3.31662479 Simplifying t + -5 = 3.31662479 Reorder the terms: -5 + t = 3.31662479 Solving -5 + t = 3.31662479 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + t = 3.31662479 + 5 t = 3.31662479 + 5 Combine like terms: 3.31662479 + 5 = 8.31662479 t = 8.31662479 Simplifying t = 8.31662479

Subproblem 2

t + -5 = -3.31662479 Simplifying t + -5 = -3.31662479 Reorder the terms: -5 + t = -3.31662479 Solving -5 + t = -3.31662479 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -3.31662479 + 5 Combine like terms: -5 + 5 = 0 0 + t = -3.31662479 + 5 t = -3.31662479 + 5 Combine like terms: -3.31662479 + 5 = 1.68337521 t = 1.68337521 Simplifying t = 1.68337521

Solution

The solution to the problem is based on the solutions from the subproblems. t = {8.31662479, 1.68337521}

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