6t*6t-5.4-3.5t+2.5t+2.5t+3t=

Solution for 6t*6t-5.4-3.5t+2.5t+2.5t+3t= equation:

Simplifying
6t * 6t + -5.4 + -3.5t + 2.5t + 2.5t + 3t = 0

Reorder the terms for easier multiplication:
6 * 6t * t + -5.4 + -3.5t + 2.5t + 2.5t + 3t = 0

Multiply 6 * 6
36t * t + -5.4 + -3.5t + 2.5t + 2.5t + 3t = 0

Multiply t * t
36t2 + -5.4 + -3.5t + 2.5t + 2.5t + 3t = 0

Reorder the terms:
-5.4 + -3.5t + 2.5t + 2.5t + 3t + 36t2 = 0

Combine like terms: -3.5t + 2.5t = -1t
-5.4 + -1t + 2.5t + 3t + 36t2 = 0

Combine like terms: -1t + 2.5t = 1.5t
-5.4 + 1.5t + 3t + 36t2 = 0

Combine like terms: 1.5t + 3t = 4.5t
-5.4 + 4.5t + 36t2 = 0

Solving
-5.4 + 4.5t + 36t2 = 0

Solving for variable 't'.

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

Divide each side by '36'.
-0.15 + 0.125t + t2 = 0

Move the constant term to the right:

Add '0.15' to each side of the equation.
-0.15 + 0.125t + 0.15 + t2 = 0 + 0.15

Reorder the terms:
-0.15 + 0.15 + 0.125t + t2 = 0 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + 0.125t + t2 = 0 + 0.15
0.125t + t2 = 0 + 0.15

Combine like terms: 0 + 0.15 = 0.15
0.125t + t2 = 0.15

The t term is 0.125t.  Take half its coefficient (0.0625).
Square it (0.00390625) and add it to both sides.

Add '0.00390625' to each side of the equation.
0.125t + 0.00390625 + t2 = 0.15 + 0.00390625

Reorder the terms:
0.00390625 + 0.125t + t2 = 0.15 + 0.00390625

Combine like terms: 0.15 + 0.00390625 = 0.15390625
0.00390625 + 0.125t + t2 = 0.15390625

Factor a perfect square on the left side:
(t + 0.0625)(t + 0.0625) = 0.15390625

Calculate the square root of the right side: 0.392308871

Break this problem into two subproblems by setting 
(t + 0.0625) equal to 0.392308871 and -0.392308871.

Subproblem 1
t + 0.0625 = 0.392308871

Simplifying
t + 0.0625 = 0.392308871

Reorder the terms:
0.0625 + t = 0.392308871

Solving
0.0625 + t = 0.392308871

Solving for variable 't'.

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

Add '-0.0625' to each side of the equation.
0.0625 + -0.0625 + t = 0.392308871 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + t = 0.392308871 + -0.0625
t = 0.392308871 + -0.0625

Combine like terms: 0.392308871 + -0.0625 = 0.329808871
t = 0.329808871

Simplifying
t = 0.329808871

Subproblem 2
t + 0.0625 = -0.392308871

Simplifying
t + 0.0625 = -0.392308871

Reorder the terms:
0.0625 + t = -0.392308871

Solving
0.0625 + t = -0.392308871

Solving for variable 't'.

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

Add '-0.0625' to each side of the equation.
0.0625 + -0.0625 + t = -0.392308871 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + t = -0.392308871 + -0.0625
t = -0.392308871 + -0.0625

Combine like terms: -0.392308871 + -0.0625 = -0.454808871
t = -0.454808871

Simplifying
t = -0.454808871

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.329808871, -0.454808871}