5(t-3)2t=-30

Solution for 5(t-3)2t=-30 equation:

Simplifying
5(t + -3) * 2t = -30

Reorder the terms:
5(-3 + t) * 2t = -30

Reorder the terms for easier multiplication:
5 * 2t(-3 + t) = -30

Multiply 5 * 2
10t(-3 + t) = -30
(-3 * 10t + t * 10t) = -30
(-30t + 10t2) = -30

Solving
-30t + 10t2 = -30

Solving for variable 't'.

Reorder the terms:
30 + -30t + 10t2 = -30 + 30

Combine like terms: -30 + 30 = 0
30 + -30t + 10t2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(3 + -3t + t2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(3 + -3t + t2)' equal to zero and attempt to solve:

Simplifying
3 + -3t + t2 = 0

Solving
3 + -3t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -3t + -3 + t2 = 0 + -3

Reorder the terms:
3 + -3 + -3t + t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -3t + t2 = 0 + -3
-3t + t2 = 0 + -3

Combine like terms: 0 + -3 = -3
-3t + t2 = -3

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = -3 + 2.25

Reorder the terms:
2.25 + -3t + t2 = -3 + 2.25

Combine like terms: -3 + 2.25 = -0.75
2.25 + -3t + t2 = -0.75

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = -0.75

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.