2t^2+40t=42

Solution for 2t^2+40t=42 equation:

Simplifying
2t2 + 40t = 42

Reorder the terms:
40t + 2t2 = 42

Solving
40t + 2t2 = 42

Solving for variable 't'.

Reorder the terms:
-42 + 40t + 2t2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 40t + 2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 20t + t2) = 0

Factor a trinomial.
2((-21 + -1t)(1 + -1t)) = 0

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

Simplifying
-21 + -1t = 0

Solving
-21 + -1t = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1t = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1t = 0 + 21
-1t = 0 + 21

Combine like terms: 0 + 21 = 21
-1t = 21

Divide each side by '-1'.
t = -21

Simplifying
t = -21
Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

Solving
1 + -1t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1t = 0 + -1
-1t = 0 + -1

Combine like terms: 0 + -1 = -1
-1t = -1

Divide each side by '-1'.
t = 1

Simplifying
t = 1
Solution
t = {-21, 1}