40=t(t-6)

Solution for 40=t(t-6) equation:

Simplifying
40 = t(t + -6)

Reorder the terms:
40 = t(-6 + t)
40 = (-6 * t + t * t)
40 = (-6t + t2)

Solving
40 = -6t + t2

Solving for variable 't'.

Reorder the terms:
40 + 6t + -1t2 = -6t + 6t + t2 + -1t2

Combine like terms: -6t + 6t = 0
40 + 6t + -1t2 = 0 + t2 + -1t2
40 + 6t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
40 + 6t + -1t2 = 0

Factor a trinomial.
(10 + -1t)(4 + t) = 0

Subproblem 1
Set the factor '(10 + -1t)' equal to zero and attempt to solve:

Simplifying
10 + -1t = 0

Solving
10 + -1t = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1t = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1t = 0 + -10
-1t = 0 + -10

Combine like terms: 0 + -10 = -10
-1t = -10

Divide each side by '-1'.
t = 10

Simplifying
t = 10
Subproblem 2
Set the factor '(4 + t)' equal to zero and attempt to solve:

Simplifying
4 + t = 0

Solving
4 + t = 0

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

Add '-4' to each side of the equation.
4 + -4 + t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + t = 0 + -4
t = 0 + -4

Combine like terms: 0 + -4 = -4
t = -4

Simplifying
t = -4
Solution
t = {10, -4}