6t+3t(5t-4)=12(2t-5)

Solution for 6t+3t(5t-4)=12(2t-5) equation:

Simplifying
6t + 3t(5t + -4) = 12(2t + -5)

Reorder the terms:
6t + 3t(-4 + 5t) = 12(2t + -5)
6t + (-4 * 3t + 5t * 3t) = 12(2t + -5)
6t + (-12t + 15t2) = 12(2t + -5)

Combine like terms: 6t + -12t = -6t
-6t + 15t2 = 12(2t + -5)

Reorder the terms:
-6t + 15t2 = 12(-5 + 2t)
-6t + 15t2 = (-5 * 12 + 2t * 12)
-6t + 15t2 = (-60 + 24t)

Solving
-6t + 15t2 = -60 + 24t

Solving for variable 't'.

Reorder the terms:
60 + -6t + -24t + 15t2 = -60 + 24t + 60 + -24t

Combine like terms: -6t + -24t = -30t
60 + -30t + 15t2 = -60 + 24t + 60 + -24t

Reorder the terms:
60 + -30t + 15t2 = -60 + 60 + 24t + -24t

Combine like terms: -60 + 60 = 0
60 + -30t + 15t2 = 0 + 24t + -24t
60 + -30t + 15t2 = 24t + -24t

Combine like terms: 24t + -24t = 0
60 + -30t + 15t2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(4 + -2t + t2) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(4 + -2t + t2)' equal to zero and attempt to solve:

Simplifying
4 + -2t + t2 = 0

Solving
4 + -2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -2t + -4 + t2 = 0 + -4

Reorder the terms:
4 + -4 + -2t + t2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -2t + t2 = 0 + -4
-2t + t2 = 0 + -4

Combine like terms: 0 + -4 = -4
-2t + t2 = -4

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = -4 + 1

Reorder the terms:
1 + -2t + t2 = -4 + 1

Combine like terms: -4 + 1 = -3
1 + -2t + t2 = -3

Factor a perfect square on the left side:
(t + -1)(t + -1) = -3

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.