7(t+5t-9)+t=t(7t-2)+13

Solution for 7(t+5t-9)+t=t(7t-2)+13 equation:

Simplifying
7(t + 5t + -9) + t = t(7t + -2) + 13

Reorder the terms:
7(-9 + t + 5t) + t = t(7t + -2) + 13

Combine like terms: t + 5t = 6t
7(-9 + 6t) + t = t(7t + -2) + 13
(-9 * 7 + 6t * 7) + t = t(7t + -2) + 13
(-63 + 42t) + t = t(7t + -2) + 13

Combine like terms: 42t + t = 43t
-63 + 43t = t(7t + -2) + 13

Reorder the terms:
-63 + 43t = t(-2 + 7t) + 13
-63 + 43t = (-2 * t + 7t * t) + 13
-63 + 43t = (-2t + 7t2) + 13

Reorder the terms:
-63 + 43t = 13 + -2t + 7t2

Solving
-63 + 43t = 13 + -2t + 7t2

Solving for variable 't'.

Reorder the terms:
-63 + -13 + 43t + 2t + -7t2 = 13 + -2t + 7t2 + -13 + 2t + -7t2

Combine like terms: -63 + -13 = -76
-76 + 43t + 2t + -7t2 = 13 + -2t + 7t2 + -13 + 2t + -7t2

Combine like terms: 43t + 2t = 45t
-76 + 45t + -7t2 = 13 + -2t + 7t2 + -13 + 2t + -7t2

Reorder the terms:
-76 + 45t + -7t2 = 13 + -13 + -2t + 2t + 7t2 + -7t2

Combine like terms: 13 + -13 = 0
-76 + 45t + -7t2 = 0 + -2t + 2t + 7t2 + -7t2
-76 + 45t + -7t2 = -2t + 2t + 7t2 + -7t2

Combine like terms: -2t + 2t = 0
-76 + 45t + -7t2 = 0 + 7t2 + -7t2
-76 + 45t + -7t2 = 7t2 + -7t2

Combine like terms: 7t2 + -7t2 = 0
-76 + 45t + -7t2 = 0

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

Divide each side by '-7'.
10.85714286 + -6.428571429t + t2 = 0

Move the constant term to the right:

Add '-10.85714286' to each side of the equation.
10.85714286 + -6.428571429t + -10.85714286 + t2 = 0 + -10.85714286

Reorder the terms:
10.85714286 + -10.85714286 + -6.428571429t + t2 = 0 + -10.85714286

Combine like terms: 10.85714286 + -10.85714286 = 0.00000000
0.00000000 + -6.428571429t + t2 = 0 + -10.85714286
-6.428571429t + t2 = 0 + -10.85714286

Combine like terms: 0 + -10.85714286 = -10.85714286
-6.428571429t + t2 = -10.85714286

The t term is -6.428571429t.  Take half its coefficient (-3.214285715).
Square it (10.33163266) and add it to both sides.

Add '10.33163266' to each side of the equation.
-6.428571429t + 10.33163266 + t2 = -10.85714286 + 10.33163266

Reorder the terms:
10.33163266 + -6.428571429t + t2 = -10.85714286 + 10.33163266

Combine like terms: -10.85714286 + 10.33163266 = -0.5255102
10.33163266 + -6.428571429t + t2 = -0.5255102

Factor a perfect square on the left side:
(t + -3.214285715)(t + -3.214285715) = -0.5255102

Can't calculate square root of the right side.

The solution to this equation could not be determined.