10(t^2-4t-3)=0

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Solution for 10(t^2-4t-3)=0 equation: 


Simplifying
10(t2 + -4t + -3) = 0

Reorder the terms:
10(-3 + -4t + t2) = 0
(-3 * 10 + -4t * 10 + t2 * 10) = 0
(-30 + -40t + 10t2) = 0

Solving
-30 + -40t + 10t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-3 + -4t + t2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-3 + -4t + t2)' equal to zero and attempt to solve:

Simplifying
-3 + -4t + t2 = 0

Solving
-3 + -4t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -4t + 3 + t2 = 0 + 3

Reorder the terms:
-3 + 3 + -4t + t2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4t + t2 = 0 + 3
-4t + t2 = 0 + 3

Combine like terms: 0 + 3 = 3
-4t + t2 = 3

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = 3 + 4

Reorder the terms:
4 + -4t + t2 = 3 + 4

Combine like terms: 3 + 4 = 7
4 + -4t + t2 = 7

Factor a perfect square on the left side:
(t + -2)(t + -2) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(t + -2) equal to 2.645751311 and -2.645751311.


Subproblem 1
t + -2 = 2.645751311

Simplifying
t + -2 = 2.645751311

Reorder the terms:
-2 + t = 2.645751311

Solving
-2 + t = 2.645751311

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = 2.645751311 + 2

Combine like terms: -2 + 2 = 0
0 + t = 2.645751311 + 2
t = 2.645751311 + 2

Combine like terms: 2.645751311 + 2 = 4.645751311
t = 4.645751311

Simplifying
t = 4.645751311


Subproblem 2
t + -2 = -2.645751311

Simplifying
t + -2 = -2.645751311

Reorder the terms:
-2 + t = -2.645751311

Solving
-2 + t = -2.645751311

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = -2.645751311 + 2

Combine like terms: -2 + 2 = 0
0 + t = -2.645751311 + 2
t = -2.645751311 + 2

Combine like terms: -2.645751311 + 2 = -0.645751311
t = -0.645751311

Simplifying
t = -0.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.645751311, -0.645751311}
Solution
t = {4.645751311, -0.645751311}

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