15t+4(2t+3)=10-[4t(t-1)]

Solution for 15t+4(2t+3)=10-[4t(t-1)] equation:

Simplifying
15t + 4(2t + 3) = 10 + -1[4t(t + -1)]

Reorder the terms:
15t + 4(3 + 2t) = 10 + -1[4t(t + -1)]
15t + (3 * 4 + 2t * 4) = 10 + -1[4t(t + -1)]
15t + (12 + 8t) = 10 + -1[4t(t + -1)]

Reorder the terms:
12 + 15t + 8t = 10 + -1[4t(t + -1)]

Combine like terms: 15t + 8t = 23t
12 + 23t = 10 + -1[4t(t + -1)]

Reorder the terms:
12 + 23t = 10 + -1[4t(-1 + t)]
12 + 23t = 10 + -1[(-1 * 4t + t * 4t)]
12 + 23t = 10 + -1[(-4t + 4t2)]
12 + 23t = 10 + [-4t * -1 + 4t2 * -1]
12 + 23t = 10 + [4t + -4t2]

Solving
12 + 23t = 10 + 4t + -4t2

Solving for variable 't'.

Reorder the terms:
12 + -10 + 23t + -4t + 4t2 = 10 + 4t + -4t2 + -10 + -4t + 4t2

Combine like terms: 12 + -10 = 2
2 + 23t + -4t + 4t2 = 10 + 4t + -4t2 + -10 + -4t + 4t2

Combine like terms: 23t + -4t = 19t
2 + 19t + 4t2 = 10 + 4t + -4t2 + -10 + -4t + 4t2

Reorder the terms:
2 + 19t + 4t2 = 10 + -10 + 4t + -4t + -4t2 + 4t2

Combine like terms: 10 + -10 = 0
2 + 19t + 4t2 = 0 + 4t + -4t + -4t2 + 4t2
2 + 19t + 4t2 = 4t + -4t + -4t2 + 4t2

Combine like terms: 4t + -4t = 0
2 + 19t + 4t2 = 0 + -4t2 + 4t2
2 + 19t + 4t2 = -4t2 + 4t2

Combine like terms: -4t2 + 4t2 = 0
2 + 19t + 4t2 = 0

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

Divide each side by '4'.
0.5 + 4.75t + t2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 4.75t + -0.5 + t2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 4.75t + t2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 4.75t + t2 = 0 + -0.5
4.75t + t2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
4.75t + t2 = -0.5

The t term is 4.75t.  Take half its coefficient (2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
4.75t + 5.640625 + t2 = -0.5 + 5.640625

Reorder the terms:
5.640625 + 4.75t + t2 = -0.5 + 5.640625

Combine like terms: -0.5 + 5.640625 = 5.140625
5.640625 + 4.75t + t2 = 5.140625

Factor a perfect square on the left side:
(t + 2.375)(t + 2.375) = 5.140625

Calculate the square root of the right side: 2.267294643

Break this problem into two subproblems by setting 
(t + 2.375) equal to 2.267294643 and -2.267294643.

Subproblem 1
t + 2.375 = 2.267294643

Simplifying
t + 2.375 = 2.267294643

Reorder the terms:
2.375 + t = 2.267294643

Solving
2.375 + t = 2.267294643

Solving for variable 't'.

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

Add '-2.375' to each side of the equation.
2.375 + -2.375 + t = 2.267294643 + -2.375

Combine like terms: 2.375 + -2.375 = 0.000
0.000 + t = 2.267294643 + -2.375
t = 2.267294643 + -2.375

Combine like terms: 2.267294643 + -2.375 = -0.107705357
t = -0.107705357

Simplifying
t = -0.107705357

Subproblem 2
t + 2.375 = -2.267294643

Simplifying
t + 2.375 = -2.267294643

Reorder the terms:
2.375 + t = -2.267294643

Solving
2.375 + t = -2.267294643

Solving for variable 't'.

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

Add '-2.375' to each side of the equation.
2.375 + -2.375 + t = -2.267294643 + -2.375

Combine like terms: 2.375 + -2.375 = 0.000
0.000 + t = -2.267294643 + -2.375
t = -2.267294643 + -2.375

Combine like terms: -2.267294643 + -2.375 = -4.642294643
t = -4.642294643

Simplifying
t = -4.642294643

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.107705357, -4.642294643}