42=18t+4t(t+5)

Solution for 42=18t+4t(t+5) equation:

Simplifying
42 = 18t + 4t(t + 5)

Reorder the terms:
42 = 18t + 4t(5 + t)
42 = 18t + (5 * 4t + t * 4t)
42 = 18t + (20t + 4t2)

Combine like terms: 18t + 20t = 38t
42 = 38t + 4t2

Solving
42 = 38t + 4t2

Solving for variable 't'.

Reorder the terms:
42 + -38t + -4t2 = 38t + -38t + 4t2 + -4t2

Combine like terms: 38t + -38t = 0
42 + -38t + -4t2 = 0 + 4t2 + -4t2
42 + -38t + -4t2 = 4t2 + -4t2

Combine like terms: 4t2 + -4t2 = 0
42 + -38t + -4t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -19t + -2t2) = 0

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

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

Simplifying
21 + 2t = 0

Solving
21 + 2t = 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 + 2t = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 2t = 0 + -21
2t = 0 + -21

Combine like terms: 0 + -21 = -21
2t = -21

Divide each side by '2'.
t = -10.5

Simplifying
t = -10.5
Solution
t = {1, -10.5}