8(3t+4)10t-3+7(2t+5)=

Solution for 8(3t+4)10t-3+7(2t+5)= equation:

Simplifying
8(3t + 4) * 10t + -3 + 7(2t + 5) = 0

Reorder the terms:
8(4 + 3t) * 10t + -3 + 7(2t + 5) = 0

Reorder the terms for easier multiplication:
8 * 10t(4 + 3t) + -3 + 7(2t + 5) = 0

Multiply 8 * 10
80t(4 + 3t) + -3 + 7(2t + 5) = 0
(4 * 80t + 3t * 80t) + -3 + 7(2t + 5) = 0
(320t + 240t2) + -3 + 7(2t + 5) = 0

Reorder the terms:
320t + 240t2 + -3 + 7(5 + 2t) = 0
320t + 240t2 + -3 + (5 * 7 + 2t * 7) = 0
320t + 240t2 + -3 + (35 + 14t) = 0

Reorder the terms:
-3 + 35 + 320t + 14t + 240t2 = 0

Combine like terms: -3 + 35 = 32
32 + 320t + 14t + 240t2 = 0

Combine like terms: 320t + 14t = 334t
32 + 334t + 240t2 = 0

Solving
32 + 334t + 240t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 167t + 120t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(16 + 167t + 120t2)' equal to zero and attempt to solve:

Simplifying
16 + 167t + 120t2 = 0

Solving
16 + 167t + 120t2 = 0

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

Divide each side by '120'.
0.1333333333 + 1.391666667t + t2 = 0.0

Move the constant term to the right:

Add '-0.1333333333' to each side of the equation.
0.1333333333 + 1.391666667t + -0.1333333333 + t2 = 0.0 + -0.1333333333

Reorder the terms:
0.1333333333 + -0.1333333333 + 1.391666667t + t2 = 0.0 + -0.1333333333

Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000
0.0000000000 + 1.391666667t + t2 = 0.0 + -0.1333333333
1.391666667t + t2 = 0.0 + -0.1333333333

Combine like terms: 0.0 + -0.1333333333 = -0.1333333333
1.391666667t + t2 = -0.1333333333

The t term is 1.391666667t.  Take half its coefficient (0.6958333335).
Square it (0.4841840280) and add it to both sides.

Add '0.4841840280' to each side of the equation.
1.391666667t + 0.4841840280 + t2 = -0.1333333333 + 0.4841840280

Reorder the terms:
0.4841840280 + 1.391666667t + t2 = -0.1333333333 + 0.4841840280

Combine like terms: -0.1333333333 + 0.4841840280 = 0.3508506947
0.4841840280 + 1.391666667t + t2 = 0.3508506947

Factor a perfect square on the left side:
(t + 0.6958333335)(t + 0.6958333335) = 0.3508506947

Calculate the square root of the right side: 0.59232651

Break this problem into two subproblems by setting 
(t + 0.6958333335) equal to 0.59232651 and -0.59232651.

Subproblem 1
t + 0.6958333335 = 0.59232651

Simplifying
t + 0.6958333335 = 0.59232651

Reorder the terms:
0.6958333335 + t = 0.59232651

Solving
0.6958333335 + t = 0.59232651

Solving for variable 't'.

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

Add '-0.6958333335' to each side of the equation.
0.6958333335 + -0.6958333335 + t = 0.59232651 + -0.6958333335

Combine like terms: 0.6958333335 + -0.6958333335 = 0.0000000000
0.0000000000 + t = 0.59232651 + -0.6958333335
t = 0.59232651 + -0.6958333335

Combine like terms: 0.59232651 + -0.6958333335 = -0.1035068235
t = -0.1035068235

Simplifying
t = -0.1035068235

Subproblem 2
t + 0.6958333335 = -0.59232651

Simplifying
t + 0.6958333335 = -0.59232651

Reorder the terms:
0.6958333335 + t = -0.59232651

Solving
0.6958333335 + t = -0.59232651

Solving for variable 't'.

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

Add '-0.6958333335' to each side of the equation.
0.6958333335 + -0.6958333335 + t = -0.59232651 + -0.6958333335

Combine like terms: 0.6958333335 + -0.6958333335 = 0.0000000000
0.0000000000 + t = -0.59232651 + -0.6958333335
t = -0.59232651 + -0.6958333335

Combine like terms: -0.59232651 + -0.6958333335 = -1.2881598435
t = -1.2881598435

Simplifying
t = -1.2881598435

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.1035068235, -1.2881598435}
Solution
t = {-0.1035068235, -1.2881598435}