-6t(-7t+9)=10

Solution for -6t(-7t+9)=10 equation:

Simplifying
-6t(-7t + 9) = 10

Reorder the terms:
-6t(9 + -7t) = 10
(9 * -6t + -7t * -6t) = 10
(-54t + 42t2) = 10

Solving
-54t + 42t2 = 10

Solving for variable 't'.

Reorder the terms:
-10 + -54t + 42t2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -54t + 42t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -27t + 21t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -27t + 21t2)' equal to zero and attempt to solve:

Simplifying
-5 + -27t + 21t2 = 0

Solving
-5 + -27t + 21t2 = 0

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

Divide each side by '21'.
-0.2380952381 + -1.285714286t + t2 = 0

Move the constant term to the right:

Add '0.2380952381' to each side of the equation.
-0.2380952381 + -1.285714286t + 0.2380952381 + t2 = 0 + 0.2380952381

Reorder the terms:
-0.2380952381 + 0.2380952381 + -1.285714286t + t2 = 0 + 0.2380952381

Combine like terms: -0.2380952381 + 0.2380952381 = 0.0000000000
0.0000000000 + -1.285714286t + t2 = 0 + 0.2380952381
-1.285714286t + t2 = 0 + 0.2380952381

Combine like terms: 0 + 0.2380952381 = 0.2380952381
-1.285714286t + t2 = 0.2380952381

The t term is -1.285714286t.  Take half its coefficient (-0.642857143).
Square it (0.4132653063) and add it to both sides.

Add '0.4132653063' to each side of the equation.
-1.285714286t + 0.4132653063 + t2 = 0.2380952381 + 0.4132653063

Reorder the terms:
0.4132653063 + -1.285714286t + t2 = 0.2380952381 + 0.4132653063

Combine like terms: 0.2380952381 + 0.4132653063 = 0.6513605444
0.4132653063 + -1.285714286t + t2 = 0.6513605444

Factor a perfect square on the left side:
(t + -0.642857143)(t + -0.642857143) = 0.6513605444

Calculate the square root of the right side: 0.807069108

Break this problem into two subproblems by setting 
(t + -0.642857143) equal to 0.807069108 and -0.807069108.

Subproblem 1
t + -0.642857143 = 0.807069108

Simplifying
t + -0.642857143 = 0.807069108

Reorder the terms:
-0.642857143 + t = 0.807069108

Solving
-0.642857143 + t = 0.807069108

Solving for variable 't'.

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

Add '0.642857143' to each side of the equation.
-0.642857143 + 0.642857143 + t = 0.807069108 + 0.642857143

Combine like terms: -0.642857143 + 0.642857143 = 0.000000000
0.000000000 + t = 0.807069108 + 0.642857143
t = 0.807069108 + 0.642857143

Combine like terms: 0.807069108 + 0.642857143 = 1.449926251
t = 1.449926251

Simplifying
t = 1.449926251

Subproblem 2
t + -0.642857143 = -0.807069108

Simplifying
t + -0.642857143 = -0.807069108

Reorder the terms:
-0.642857143 + t = -0.807069108

Solving
-0.642857143 + t = -0.807069108

Solving for variable 't'.

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

Add '0.642857143' to each side of the equation.
-0.642857143 + 0.642857143 + t = -0.807069108 + 0.642857143

Combine like terms: -0.642857143 + 0.642857143 = 0.000000000
0.000000000 + t = -0.807069108 + 0.642857143
t = -0.807069108 + 0.642857143

Combine like terms: -0.807069108 + 0.642857143 = -0.164211965
t = -0.164211965

Simplifying
t = -0.164211965

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.449926251, -0.164211965}
Solution
t = {1.449926251, -0.164211965}