t(t-1)=42

Solution for t(t-1)=42 equation:

Simplifying
t(t + -1) = 42

Reorder the terms:
t(-1 + t) = 42
(-1 * t + t * t) = 42
(-1t + t2) = 42

Solving
-1t + t2 = 42

Solving for variable 't'.

Reorder the terms:
-42 + -1t + t2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + -1t + t2 = 0

Factor a trinomial.
(-6 + -1t)(7 + -1t) = 0

Subproblem 1
Set the factor '(-6 + -1t)' equal to zero and attempt to solve:

Simplifying
-6 + -1t = 0

Solving
-6 + -1t = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1t = 0 + 6
-1t = 0 + 6

Combine like terms: 0 + 6 = 6
-1t = 6

Divide each side by '-1'.
t = -6

Simplifying
t = -6
Subproblem 2
Set the factor '(7 + -1t)' equal to zero and attempt to solve:

Simplifying
7 + -1t = 0

Solving
7 + -1t = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1t = 0 + -7
-1t = 0 + -7

Combine like terms: 0 + -7 = -7
-1t = -7

Divide each side by '-1'.
t = 7

Simplifying
t = 7
Solution
t = {-6, 7}