7t(t-5)+7t=7(2t+5)-9

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Solution for 7t(t-5)+7t=7(2t+5)-9 equation:


Simplifying
7t(t + -5) + 7t = 7(2t + 5) + -9

Reorder the terms:
7t(-5 + t) + 7t = 7(2t + 5) + -9
(-5 * 7t + t * 7t) + 7t = 7(2t + 5) + -9
(-35t + 7t2) + 7t = 7(2t + 5) + -9

Reorder the terms:
-35t + 7t + 7t2 = 7(2t + 5) + -9

Combine like terms: -35t + 7t = -28t
-28t + 7t2 = 7(2t + 5) + -9

Reorder the terms:
-28t + 7t2 = 7(5 + 2t) + -9
-28t + 7t2 = (5 * 7 + 2t * 7) + -9
-28t + 7t2 = (35 + 14t) + -9

Reorder the terms:
-28t + 7t2 = 35 + -9 + 14t

Combine like terms: 35 + -9 = 26
-28t + 7t2 = 26 + 14t

Solving
-28t + 7t2 = 26 + 14t

Solving for variable 't'.

Reorder the terms:
-26 + -28t + -14t + 7t2 = 26 + 14t + -26 + -14t

Combine like terms: -28t + -14t = -42t
-26 + -42t + 7t2 = 26 + 14t + -26 + -14t

Reorder the terms:
-26 + -42t + 7t2 = 26 + -26 + 14t + -14t

Combine like terms: 26 + -26 = 0
-26 + -42t + 7t2 = 0 + 14t + -14t
-26 + -42t + 7t2 = 14t + -14t

Combine like terms: 14t + -14t = 0
-26 + -42t + 7t2 = 0

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

Divide each side by '7'.
-3.714285714 + -6t + t2 = 0

Move the constant term to the right:

Add '3.714285714' to each side of the equation.
-3.714285714 + -6t + 3.714285714 + t2 = 0 + 3.714285714

Reorder the terms:
-3.714285714 + 3.714285714 + -6t + t2 = 0 + 3.714285714

Combine like terms: -3.714285714 + 3.714285714 = 0.000000000
0.000000000 + -6t + t2 = 0 + 3.714285714
-6t + t2 = 0 + 3.714285714

Combine like terms: 0 + 3.714285714 = 3.714285714
-6t + t2 = 3.714285714

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 = 3.714285714 + 9

Reorder the terms:
9 + -6t + t2 = 3.714285714 + 9

Combine like terms: 3.714285714 + 9 = 12.714285714
9 + -6t + t2 = 12.714285714

Factor a perfect square on the left side:
(t + -3)(t + -3) = 12.714285714

Calculate the square root of the right side: 3.565709707

Break this problem into two subproblems by setting 
(t + -3) equal to 3.565709707 and -3.565709707.

Subproblem 1

t + -3 = 3.565709707 Simplifying t + -3 = 3.565709707 Reorder the terms: -3 + t = 3.565709707 Solving -3 + t = 3.565709707 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 = 3.565709707 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.565709707 + 3 t = 3.565709707 + 3 Combine like terms: 3.565709707 + 3 = 6.565709707 t = 6.565709707 Simplifying t = 6.565709707

Subproblem 2

t + -3 = -3.565709707 Simplifying t + -3 = -3.565709707 Reorder the terms: -3 + t = -3.565709707 Solving -3 + t = -3.565709707 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 = -3.565709707 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.565709707 + 3 t = -3.565709707 + 3 Combine like terms: -3.565709707 + 3 = -0.565709707 t = -0.565709707 Simplifying t = -0.565709707

Solution

The solution to the problem is based on the solutions from the subproblems. t = {6.565709707, -0.565709707}

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