16t^2-30t-18=0

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Solution for 16t^2-30t-18=0 equation: 


Simplifying
16t2 + -30t + -18 = 0

Reorder the terms:
-18 + -30t + 16t2 = 0

Solving
-18 + -30t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -15t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + -15t + 8t2)' equal to zero and attempt to solve:

Simplifying
-9 + -15t + 8t2 = 0

Solving
-9 + -15t + 8t2 = 0

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

Divide each side by '8'.
-1.125 + -1.875t + t2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + -1.875t + 1.125 + t2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + -1.875t + t2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + -1.875t + t2 = 0 + 1.125
-1.875t + t2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
-1.875t + t2 = 1.125

The t term is -1.875t.  Take half its coefficient (-0.9375).
Square it (0.87890625) and add it to both sides.

Add '0.87890625' to each side of the equation.
-1.875t + 0.87890625 + t2 = 1.125 + 0.87890625

Reorder the terms:
0.87890625 + -1.875t + t2 = 1.125 + 0.87890625

Combine like terms: 1.125 + 0.87890625 = 2.00390625
0.87890625 + -1.875t + t2 = 2.00390625

Factor a perfect square on the left side:
(t + -0.9375)(t + -0.9375) = 2.00390625

Calculate the square root of the right side: 1.415593957

Break this problem into two subproblems by setting 
(t + -0.9375) equal to 1.415593957 and -1.415593957.


Subproblem 1
t + -0.9375 = 1.415593957

Simplifying
t + -0.9375 = 1.415593957

Reorder the terms:
-0.9375 + t = 1.415593957

Solving
-0.9375 + t = 1.415593957

Solving for variable 't'.

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

Add '0.9375' to each side of the equation.
-0.9375 + 0.9375 + t = 1.415593957 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + t = 1.415593957 + 0.9375
t = 1.415593957 + 0.9375

Combine like terms: 1.415593957 + 0.9375 = 2.353093957
t = 2.353093957

Simplifying
t = 2.353093957


Subproblem 2
t + -0.9375 = -1.415593957

Simplifying
t + -0.9375 = -1.415593957

Reorder the terms:
-0.9375 + t = -1.415593957

Solving
-0.9375 + t = -1.415593957

Solving for variable 't'.

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

Add '0.9375' to each side of the equation.
-0.9375 + 0.9375 + t = -1.415593957 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + t = -1.415593957 + 0.9375
t = -1.415593957 + 0.9375

Combine like terms: -1.415593957 + 0.9375 = -0.478093957
t = -0.478093957

Simplifying
t = -0.478093957


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.353093957, -0.478093957}
Solution
t = {2.353093957, -0.478093957}

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