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

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

Simplifying
5(3t + -4) + -1(t2 + 2) + -2t(t + -3) = 0

Reorder the terms:
5(-4 + 3t) + -1(t2 + 2) + -2t(t + -3) = 0
(-4 * 5 + 3t * 5) + -1(t2 + 2) + -2t(t + -3) = 0
(-20 + 15t) + -1(t2 + 2) + -2t(t + -3) = 0

Reorder the terms:
-20 + 15t + -1(2 + t2) + -2t(t + -3) = 0
-20 + 15t + (2 * -1 + t2 * -1) + -2t(t + -3) = 0
-20 + 15t + (-2 + -1t2) + -2t(t + -3) = 0

Reorder the terms:
-20 + 15t + -2 + -1t2 + -2t(-3 + t) = 0
-20 + 15t + -2 + -1t2 + (-3 * -2t + t * -2t) = 0
-20 + 15t + -2 + -1t2 + (6t + -2t2) = 0

Reorder the terms:
-20 + -2 + 15t + 6t + -1t2 + -2t2 = 0

Combine like terms: -20 + -2 = -22
-22 + 15t + 6t + -1t2 + -2t2 = 0

Combine like terms: 15t + 6t = 21t
-22 + 21t + -1t2 + -2t2 = 0

Combine like terms: -1t2 + -2t2 = -3t2
-22 + 21t + -3t2 = 0

Solving
-22 + 21t + -3t2 = 0

Solving for variable 't'.

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

Divide each side by '-3'.
7.333333333 + -7t + t2 = 0

Move the constant term to the right:

Add '-7.333333333' to each side of the equation.
7.333333333 + -7t + -7.333333333 + t2 = 0 + -7.333333333

Reorder the terms:
7.333333333 + -7.333333333 + -7t + t2 = 0 + -7.333333333

Combine like terms: 7.333333333 + -7.333333333 = 0.000000000
0.000000000 + -7t + t2 = 0 + -7.333333333
-7t + t2 = 0 + -7.333333333

Combine like terms: 0 + -7.333333333 = -7.333333333
-7t + t2 = -7.333333333

The t term is -7t.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7t + 12.25 + t2 = -7.333333333 + 12.25

Reorder the terms:
12.25 + -7t + t2 = -7.333333333 + 12.25

Combine like terms: -7.333333333 + 12.25 = 4.916666667
12.25 + -7t + t2 = 4.916666667

Factor a perfect square on the left side:
(t + -3.5)(t + -3.5) = 4.916666667

Calculate the square root of the right side: 2.217355783

Break this problem into two subproblems by setting 
(t + -3.5) equal to 2.217355783 and -2.217355783.

Subproblem 1
t + -3.5 = 2.217355783

Simplifying
t + -3.5 = 2.217355783

Reorder the terms:
-3.5 + t = 2.217355783

Solving
-3.5 + t = 2.217355783

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = 2.217355783 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = 2.217355783 + 3.5
t = 2.217355783 + 3.5

Combine like terms: 2.217355783 + 3.5 = 5.717355783
t = 5.717355783

Simplifying
t = 5.717355783

Subproblem 2
t + -3.5 = -2.217355783

Simplifying
t + -3.5 = -2.217355783

Reorder the terms:
-3.5 + t = -2.217355783

Solving
-3.5 + t = -2.217355783

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = -2.217355783 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = -2.217355783 + 3.5
t = -2.217355783 + 3.5

Combine like terms: -2.217355783 + 3.5 = 1.282644217
t = 1.282644217

Simplifying
t = 1.282644217

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.717355783, 1.282644217}