10=t(t-9)

Solution for 10=t(t-9) equation:

Simplifying
10 = t(t + -9)

Reorder the terms:
10 = t(-9 + t)
10 = (-9 * t + t * t)
10 = (-9t + t2)

Solving
10 = -9t + t2

Solving for variable 't'.

Reorder the terms:
10 + 9t + -1t2 = -9t + 9t + t2 + -1t2

Combine like terms: -9t + 9t = 0
10 + 9t + -1t2 = 0 + t2 + -1t2
10 + 9t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
10 + 9t + -1t2 = 0

Factor a trinomial.
(10 + -1t)(1 + 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 '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 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 + t = 0 + -1

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

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

Simplifying
t = -1
Solution
t = {10, -1}