-2t^2+58t=-42

Solution for -2t^2+58t=-42 equation:

Simplifying
-2t2 + 58t = -42

Reorder the terms:
58t + -2t2 = -42

Solving
58t + -2t2 = -42

Solving for variable 't'.

Reorder the terms:
42 + 58t + -2t2 = -42 + 42

Combine like terms: -42 + 42 = 0
42 + 58t + -2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + 29t + -1t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(21 + 29t + -1t2)' equal to zero and attempt to solve:

Simplifying
21 + 29t + -1t2 = 0

Solving
21 + 29t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-21 + -29t + t2 = 0

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -29t + 21 + t2 = 0 + 21

Reorder the terms:
-21 + 21 + -29t + t2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -29t + t2 = 0 + 21
-29t + t2 = 0 + 21

Combine like terms: 0 + 21 = 21
-29t + t2 = 21

The t term is -29t.  Take half its coefficient (-14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
-29t + 210.25 + t2 = 21 + 210.25

Reorder the terms:
210.25 + -29t + t2 = 21 + 210.25

Combine like terms: 21 + 210.25 = 231.25
210.25 + -29t + t2 = 231.25

Factor a perfect square on the left side:
(t + -14.5)(t + -14.5) = 231.25

Calculate the square root of the right side: 15.206906326

Break this problem into two subproblems by setting 
(t + -14.5) equal to 15.206906326 and -15.206906326.

Subproblem 1
t + -14.5 = 15.206906326

Simplifying
t + -14.5 = 15.206906326

Reorder the terms:
-14.5 + t = 15.206906326

Solving
-14.5 + t = 15.206906326

Solving for variable 't'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + t = 15.206906326 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + t = 15.206906326 + 14.5
t = 15.206906326 + 14.5

Combine like terms: 15.206906326 + 14.5 = 29.706906326
t = 29.706906326

Simplifying
t = 29.706906326

Subproblem 2
t + -14.5 = -15.206906326

Simplifying
t + -14.5 = -15.206906326

Reorder the terms:
-14.5 + t = -15.206906326

Solving
-14.5 + t = -15.206906326

Solving for variable 't'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + t = -15.206906326 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + t = -15.206906326 + 14.5
t = -15.206906326 + 14.5

Combine like terms: -15.206906326 + 14.5 = -0.706906326
t = -0.706906326

Simplifying
t = -0.706906326

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {29.706906326, -0.706906326}
Solution
t = {29.706906326, -0.706906326}