1.4-1.6t(t+6)=4.6

Solution for 1.4-1.6t(t+6)=4.6 equation:

Simplifying
1.4 + -1.6t(t + 6) = 4.6

Reorder the terms:
1.4 + -1.6t(6 + t) = 4.6
1.4 + (6 * -1.6t + t * -1.6t) = 4.6
1.4 + (-9.6t + -1.6t2) = 4.6

Solving
1.4 + -9.6t + -1.6t2 = 4.6

Solving for variable 't'.

Reorder the terms:
1.4 + -4.6 + -9.6t + -1.6t2 = 4.6 + -4.6

Combine like terms: 1.4 + -4.6 = -3.2
-3.2 + -9.6t + -1.6t2 = 4.6 + -4.6

Combine like terms: 4.6 + -4.6 = 0.0
-3.2 + -9.6t + -1.6t2 = 0.0

Begin completing the square.  Divide all terms by
-1.6 the coefficient of the squared term: 

Divide each side by '-1.6'.
2 + 6t + t2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 6t + -2 + t2 = 0 + -2

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

Combine like terms: 2 + -2 = 0
0 + 6t + t2 = 0 + -2
6t + t2 = 0 + -2

Combine like terms: 0 + -2 = -2
6t + t2 = -2

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 = -2 + 9

Reorder the terms:
9 + 6t + t2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + 6t + t2 = 7

Factor a perfect square on the left side:
(t + 3)(t + 3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(t + 3) equal to 2.645751311 and -2.645751311.

Subproblem 1
t + 3 = 2.645751311

Simplifying
t + 3 = 2.645751311

Reorder the terms:
3 + t = 2.645751311

Solving
3 + t = 2.645751311

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 = 2.645751311 + -3

Combine like terms: 3 + -3 = 0
0 + t = 2.645751311 + -3
t = 2.645751311 + -3

Combine like terms: 2.645751311 + -3 = -0.354248689
t = -0.354248689

Simplifying
t = -0.354248689

Subproblem 2
t + 3 = -2.645751311

Simplifying
t + 3 = -2.645751311

Reorder the terms:
3 + t = -2.645751311

Solving
3 + t = -2.645751311

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 = -2.645751311 + -3

Combine like terms: 3 + -3 = 0
0 + t = -2.645751311 + -3
t = -2.645751311 + -3

Combine like terms: -2.645751311 + -3 = -5.645751311
t = -5.645751311

Simplifying
t = -5.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.354248689, -5.645751311}