-2(t+6)=5t(t+1)

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

Simplifying
-2(t + 6) = 5t(t + 1)

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

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

Solving
-12 + -2t = 5t + 5t2

Solving for variable 't'.

Combine like terms: -2t + -5t = -7t
-12 + -7t + -5t2 = 5t + 5t2 + -5t + -5t2

Reorder the terms:
-12 + -7t + -5t2 = 5t + -5t + 5t2 + -5t2

Combine like terms: 5t + -5t = 0
-12 + -7t + -5t2 = 0 + 5t2 + -5t2
-12 + -7t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
-12 + -7t + -5t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 7t + 5t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(12 + 7t + 5t2)' equal to zero and attempt to solve:

Simplifying
12 + 7t + 5t2 = 0

Solving
12 + 7t + 5t2 = 0

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

Divide each side by '5'.
2.4 + 1.4t + t2 = 0

Move the constant term to the right:

Add '-2.4' to each side of the equation.
2.4 + 1.4t + -2.4 + t2 = 0 + -2.4

Reorder the terms:
2.4 + -2.4 + 1.4t + t2 = 0 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + 1.4t + t2 = 0 + -2.4
1.4t + t2 = 0 + -2.4

Combine like terms: 0 + -2.4 = -2.4
1.4t + t2 = -2.4

The t term is 1.4t.  Take half its coefficient (0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
1.4t + 0.49 + t2 = -2.4 + 0.49

Reorder the terms:
0.49 + 1.4t + t2 = -2.4 + 0.49

Combine like terms: -2.4 + 0.49 = -1.91
0.49 + 1.4t + t2 = -1.91

Factor a perfect square on the left side:
(t + 0.7)(t + 0.7) = -1.91

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.