-5(2t^2+9t-3)=0

Solution for -5(2t^2+9t-3)=0 equation:

Simplifying
-5(2t2 + 9t + -3) = 0

Reorder the terms:
-5(-3 + 9t + 2t2) = 0
(-3 * -5 + 9t * -5 + 2t2 * -5) = 0
(15 + -45t + -10t2) = 0

Solving
15 + -45t + -10t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(3 + -9t + -2t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(3 + -9t + -2t2)' equal to zero and attempt to solve:

Simplifying
3 + -9t + -2t2 = 0

Solving
3 + -9t + -2t2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-1.5 + 4.5t + t2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 4.5t + 1.5 + t2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 4.5t + t2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 4.5t + t2 = 0 + 1.5
4.5t + t2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
4.5t + t2 = 1.5

The t term is 4.5t.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5t + 5.0625 + t2 = 1.5 + 5.0625

Reorder the terms:
5.0625 + 4.5t + t2 = 1.5 + 5.0625

Combine like terms: 1.5 + 5.0625 = 6.5625
5.0625 + 4.5t + t2 = 6.5625

Factor a perfect square on the left side:
(t + 2.25)(t + 2.25) = 6.5625

Calculate the square root of the right side: 2.561737691

Break this problem into two subproblems by setting 
(t + 2.25) equal to 2.561737691 and -2.561737691.

Subproblem 1
t + 2.25 = 2.561737691

Simplifying
t + 2.25 = 2.561737691

Reorder the terms:
2.25 + t = 2.561737691

Solving
2.25 + t = 2.561737691

Solving for variable 't'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + t = 2.561737691 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + t = 2.561737691 + -2.25
t = 2.561737691 + -2.25

Combine like terms: 2.561737691 + -2.25 = 0.311737691
t = 0.311737691

Simplifying
t = 0.311737691

Subproblem 2
t + 2.25 = -2.561737691

Simplifying
t + 2.25 = -2.561737691

Reorder the terms:
2.25 + t = -2.561737691

Solving
2.25 + t = -2.561737691

Solving for variable 't'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + t = -2.561737691 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + t = -2.561737691 + -2.25
t = -2.561737691 + -2.25

Combine like terms: -2.561737691 + -2.25 = -4.811737691
t = -4.811737691

Simplifying
t = -4.811737691

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.311737691, -4.811737691}
Solution
t = {0.311737691, -4.811737691}