14(t-5)+7t=t(3t+5)-13

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Solution for 14(t-5)+7t=t(3t+5)-13 equation: 


Simplifying
14(t + -5) + 7t = t(3t + 5) + -13

Reorder the terms:
14(-5 + t) + 7t = t(3t + 5) + -13
(-5 * 14 + t * 14) + 7t = t(3t + 5) + -13
(-70 + 14t) + 7t = t(3t + 5) + -13

Combine like terms: 14t + 7t = 21t
-70 + 21t = t(3t + 5) + -13

Reorder the terms:
-70 + 21t = t(5 + 3t) + -13
-70 + 21t = (5 * t + 3t * t) + -13
-70 + 21t = (5t + 3t2) + -13

Reorder the terms:
-70 + 21t = -13 + 5t + 3t2

Solving
-70 + 21t = -13 + 5t + 3t2

Solving for variable 't'.

Reorder the terms:
-70 + 13 + 21t + -5t + -3t2 = -13 + 5t + 3t2 + 13 + -5t + -3t2

Combine like terms: -70 + 13 = -57
-57 + 21t + -5t + -3t2 = -13 + 5t + 3t2 + 13 + -5t + -3t2

Combine like terms: 21t + -5t = 16t
-57 + 16t + -3t2 = -13 + 5t + 3t2 + 13 + -5t + -3t2

Reorder the terms:
-57 + 16t + -3t2 = -13 + 13 + 5t + -5t + 3t2 + -3t2

Combine like terms: -13 + 13 = 0
-57 + 16t + -3t2 = 0 + 5t + -5t + 3t2 + -3t2
-57 + 16t + -3t2 = 5t + -5t + 3t2 + -3t2

Combine like terms: 5t + -5t = 0
-57 + 16t + -3t2 = 0 + 3t2 + -3t2
-57 + 16t + -3t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
-57 + 16t + -3t2 = 0

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

Divide each side by '-3'.
19 + -5.333333333t + t2 = 0

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + -5.333333333t + -19 + t2 = 0 + -19

Reorder the terms:
19 + -19 + -5.333333333t + t2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -5.333333333t + t2 = 0 + -19
-5.333333333t + t2 = 0 + -19

Combine like terms: 0 + -19 = -19
-5.333333333t + t2 = -19

The t term is -5.333333333t.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333t + 7.111111113 + t2 = -19 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333t + t2 = -19 + 7.111111113

Combine like terms: -19 + 7.111111113 = -11.888888887
7.111111113 + -5.333333333t + t2 = -11.888888887

Factor a perfect square on the left side:
(t + -2.666666667)(t + -2.666666667) = -11.888888887

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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