2t(4-t)+3(5-t)=2(t+1)-2t(t-6)+(3t-1)(1-t)-3t^2

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Solution for 2t(4-t)+3(5-t)=2(t+1)-2t(t-6)+(3t-1)(1-t)-3t^2 equation: 


Simplifying
2t(4 + -1t) + 3(5 + -1t) = 2(t + 1) + -2t(t + -6) + (3t + -1)(1 + -1t) + -3t2
(4 * 2t + -1t * 2t) + 3(5 + -1t) = 2(t + 1) + -2t(t + -6) + (3t + -1)(1 + -1t) + -3t2
(8t + -2t2) + 3(5 + -1t) = 2(t + 1) + -2t(t + -6) + (3t + -1)(1 + -1t) + -3t2
8t + -2t2 + (5 * 3 + -1t * 3) = 2(t + 1) + -2t(t + -6) + (3t + -1)(1 + -1t) + -3t2
8t + -2t2 + (15 + -3t) = 2(t + 1) + -2t(t + -6) + (3t + -1)(1 + -1t) + -3t2

Reorder the terms:
15 + 8t + -3t + -2t2 = 2(t + 1) + -2t(t + -6) + (3t + -1)(1 + -1t) + -3t2

Combine like terms: 8t + -3t = 5t
15 + 5t + -2t2 = 2(t + 1) + -2t(t + -6) + (3t + -1)(1 + -1t) + -3t2

Reorder the terms:
15 + 5t + -2t2 = 2(1 + t) + -2t(t + -6) + (3t + -1)(1 + -1t) + -3t2
15 + 5t + -2t2 = (1 * 2 + t * 2) + -2t(t + -6) + (3t + -1)(1 + -1t) + -3t2
15 + 5t + -2t2 = (2 + 2t) + -2t(t + -6) + (3t + -1)(1 + -1t) + -3t2

Reorder the terms:
15 + 5t + -2t2 = 2 + 2t + -2t(-6 + t) + (3t + -1)(1 + -1t) + -3t2
15 + 5t + -2t2 = 2 + 2t + (-6 * -2t + t * -2t) + (3t + -1)(1 + -1t) + -3t2
15 + 5t + -2t2 = 2 + 2t + (12t + -2t2) + (3t + -1)(1 + -1t) + -3t2

Reorder the terms:
15 + 5t + -2t2 = 2 + 2t + 12t + -2t2 + (-1 + 3t)(1 + -1t) + -3t2

Multiply (-1 + 3t) * (1 + -1t)
15 + 5t + -2t2 = 2 + 2t + 12t + -2t2 + (-1(1 + -1t) + 3t * (1 + -1t)) + -3t2
15 + 5t + -2t2 = 2 + 2t + 12t + -2t2 + ((1 * -1 + -1t * -1) + 3t * (1 + -1t)) + -3t2
15 + 5t + -2t2 = 2 + 2t + 12t + -2t2 + ((-1 + 1t) + 3t * (1 + -1t)) + -3t2
15 + 5t + -2t2 = 2 + 2t + 12t + -2t2 + (-1 + 1t + (1 * 3t + -1t * 3t)) + -3t2
15 + 5t + -2t2 = 2 + 2t + 12t + -2t2 + (-1 + 1t + (3t + -3t2)) + -3t2

Combine like terms: 1t + 3t = 4t
15 + 5t + -2t2 = 2 + 2t + 12t + -2t2 + (-1 + 4t + -3t2) + -3t2

Reorder the terms:
15 + 5t + -2t2 = 2 + -1 + 2t + 12t + 4t + -2t2 + -3t2 + -3t2

Combine like terms: 2 + -1 = 1
15 + 5t + -2t2 = 1 + 2t + 12t + 4t + -2t2 + -3t2 + -3t2

Combine like terms: 2t + 12t = 14t
15 + 5t + -2t2 = 1 + 14t + 4t + -2t2 + -3t2 + -3t2

Combine like terms: 14t + 4t = 18t
15 + 5t + -2t2 = 1 + 18t + -2t2 + -3t2 + -3t2

Combine like terms: -2t2 + -3t2 = -5t2
15 + 5t + -2t2 = 1 + 18t + -5t2 + -3t2

Combine like terms: -5t2 + -3t2 = -8t2
15 + 5t + -2t2 = 1 + 18t + -8t2

Solving
15 + 5t + -2t2 = 1 + 18t + -8t2

Solving for variable 't'.

Reorder the terms:
15 + -1 + 5t + -18t + -2t2 + 8t2 = 1 + 18t + -8t2 + -1 + -18t + 8t2

Combine like terms: 15 + -1 = 14
14 + 5t + -18t + -2t2 + 8t2 = 1 + 18t + -8t2 + -1 + -18t + 8t2

Combine like terms: 5t + -18t = -13t
14 + -13t + -2t2 + 8t2 = 1 + 18t + -8t2 + -1 + -18t + 8t2

Combine like terms: -2t2 + 8t2 = 6t2
14 + -13t + 6t2 = 1 + 18t + -8t2 + -1 + -18t + 8t2

Reorder the terms:
14 + -13t + 6t2 = 1 + -1 + 18t + -18t + -8t2 + 8t2

Combine like terms: 1 + -1 = 0
14 + -13t + 6t2 = 0 + 18t + -18t + -8t2 + 8t2
14 + -13t + 6t2 = 18t + -18t + -8t2 + 8t2

Combine like terms: 18t + -18t = 0
14 + -13t + 6t2 = 0 + -8t2 + 8t2
14 + -13t + 6t2 = -8t2 + 8t2

Combine like terms: -8t2 + 8t2 = 0
14 + -13t + 6t2 = 0

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

Divide each side by '6'.
2.333333333 + -2.166666667t + t2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -2.166666667t + -2.333333333 + t2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -2.166666667t + t2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -2.166666667t + t2 = 0 + -2.333333333
-2.166666667t + t2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-2.166666667t + t2 = -2.333333333

The t term is -2.166666667t.  Take half its coefficient (-1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
-2.166666667t + 1.173611113 + t2 = -2.333333333 + 1.173611113

Reorder the terms:
1.173611113 + -2.166666667t + t2 = -2.333333333 + 1.173611113

Combine like terms: -2.333333333 + 1.173611113 = -1.15972222
1.173611113 + -2.166666667t + t2 = -1.15972222

Factor a perfect square on the left side:
(t + -1.083333334)(t + -1.083333334) = -1.15972222

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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