10t(t+2)=9t-3

Solution for 10t(t+2)=9t-3 equation:

Simplifying
10t(t + 2) = 9t + -3

Reorder the terms:
10t(2 + t) = 9t + -3
(2 * 10t + t * 10t) = 9t + -3
(20t + 10t2) = 9t + -3

Reorder the terms:
20t + 10t2 = -3 + 9t

Solving
20t + 10t2 = -3 + 9t

Solving for variable 't'.

Reorder the terms:
3 + 20t + -9t + 10t2 = -3 + 9t + 3 + -9t

Combine like terms: 20t + -9t = 11t
3 + 11t + 10t2 = -3 + 9t + 3 + -9t

Reorder the terms:
3 + 11t + 10t2 = -3 + 3 + 9t + -9t

Combine like terms: -3 + 3 = 0
3 + 11t + 10t2 = 0 + 9t + -9t
3 + 11t + 10t2 = 9t + -9t

Combine like terms: 9t + -9t = 0
3 + 11t + 10t2 = 0

Factor a trinomial.
(3 + 5t)(1 + 2t) = 0

Subproblem 1
Set the factor '(3 + 5t)' equal to zero and attempt to solve:

Simplifying
3 + 5t = 0

Solving
3 + 5t = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5t = 0 + -3
5t = 0 + -3

Combine like terms: 0 + -3 = -3
5t = -3

Divide each side by '5'.
t = -0.6

Simplifying
t = -0.6
Subproblem 2
Set the factor '(1 + 2t)' equal to zero and attempt to solve:

Simplifying
1 + 2t = 0

Solving
1 + 2t = 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 + 2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2t = 0 + -1
2t = 0 + -1

Combine like terms: 0 + -1 = -1
2t = -1

Divide each side by '2'.
t = -0.5

Simplifying
t = -0.5
Solution
t = {-0.6, -0.5}