12t^2+25t-7=10

Solution for 12t^2+25t-7=10 equation:

Simplifying
12t2 + 25t + -7 = 10

Reorder the terms:
-7 + 25t + 12t2 = 10

Solving
-7 + 25t + 12t2 = 10

Solving for variable 't'.

Reorder the terms:
-7 + -10 + 25t + 12t2 = 10 + -10

Combine like terms: -7 + -10 = -17
-17 + 25t + 12t2 = 10 + -10

Combine like terms: 10 + -10 = 0
-17 + 25t + 12t2 = 0

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

Divide each side by '12'.
-1.416666667 + 2.083333333t + t2 = 0

Move the constant term to the right:

Add '1.416666667' to each side of the equation.
-1.416666667 + 2.083333333t + 1.416666667 + t2 = 0 + 1.416666667

Reorder the terms:
-1.416666667 + 1.416666667 + 2.083333333t + t2 = 0 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + 2.083333333t + t2 = 0 + 1.416666667
2.083333333t + t2 = 0 + 1.416666667

Combine like terms: 0 + 1.416666667 = 1.416666667
2.083333333t + t2 = 1.416666667

The t term is 2.083333333t.  Take half its coefficient (1.041666667).
Square it (1.085069445) and add it to both sides.

Add '1.085069445' to each side of the equation.
2.083333333t + 1.085069445 + t2 = 1.416666667 + 1.085069445

Reorder the terms:
1.085069445 + 2.083333333t + t2 = 1.416666667 + 1.085069445

Combine like terms: 1.416666667 + 1.085069445 = 2.501736112
1.085069445 + 2.083333333t + t2 = 2.501736112

Factor a perfect square on the left side:
(t + 1.041666667)(t + 1.041666667) = 2.501736112

Calculate the square root of the right side: 1.581687742

Break this problem into two subproblems by setting 
(t + 1.041666667) equal to 1.581687742 and -1.581687742.

Subproblem 1
t + 1.041666667 = 1.581687742

Simplifying
t + 1.041666667 = 1.581687742

Reorder the terms:
1.041666667 + t = 1.581687742

Solving
1.041666667 + t = 1.581687742

Solving for variable 't'.

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

Add '-1.041666667' to each side of the equation.
1.041666667 + -1.041666667 + t = 1.581687742 + -1.041666667

Combine like terms: 1.041666667 + -1.041666667 = 0.000000000
0.000000000 + t = 1.581687742 + -1.041666667
t = 1.581687742 + -1.041666667

Combine like terms: 1.581687742 + -1.041666667 = 0.540021075
t = 0.540021075

Simplifying
t = 0.540021075

Subproblem 2
t + 1.041666667 = -1.581687742

Simplifying
t + 1.041666667 = -1.581687742

Reorder the terms:
1.041666667 + t = -1.581687742

Solving
1.041666667 + t = -1.581687742

Solving for variable 't'.

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

Add '-1.041666667' to each side of the equation.
1.041666667 + -1.041666667 + t = -1.581687742 + -1.041666667

Combine like terms: 1.041666667 + -1.041666667 = 0.000000000
0.000000000 + t = -1.581687742 + -1.041666667
t = -1.581687742 + -1.041666667

Combine like terms: -1.581687742 + -1.041666667 = -2.623354409
t = -2.623354409

Simplifying
t = -2.623354409

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.540021075, -2.623354409}