20t(t+1)=7t-2

Solution for 20t(t+1)=7t-2 equation:

Simplifying
20t(t + 1) = 7t + -2

Reorder the terms:
20t(1 + t) = 7t + -2
(1 * 20t + t * 20t) = 7t + -2
(20t + 20t2) = 7t + -2

Reorder the terms:
20t + 20t2 = -2 + 7t

Solving
20t + 20t2 = -2 + 7t

Solving for variable 't'.

Reorder the terms:
2 + 20t + -7t + 20t2 = -2 + 7t + 2 + -7t

Combine like terms: 20t + -7t = 13t
2 + 13t + 20t2 = -2 + 7t + 2 + -7t

Reorder the terms:
2 + 13t + 20t2 = -2 + 2 + 7t + -7t

Combine like terms: -2 + 2 = 0
2 + 13t + 20t2 = 0 + 7t + -7t
2 + 13t + 20t2 = 7t + -7t

Combine like terms: 7t + -7t = 0
2 + 13t + 20t2 = 0

Factor a trinomial.
(2 + 5t)(1 + 4t) = 0

Subproblem 1
Set the factor '(2 + 5t)' equal to zero and attempt to solve:

Simplifying
2 + 5t = 0

Solving
2 + 5t = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5t = 0 + -2
5t = 0 + -2

Combine like terms: 0 + -2 = -2
5t = -2

Divide each side by '5'.
t = -0.4

Simplifying
t = -0.4
Subproblem 2
Set the factor '(1 + 4t)' equal to zero and attempt to solve:

Simplifying
1 + 4t = 0

Solving
1 + 4t = 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 + 4t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4t = 0 + -1
4t = 0 + -1

Combine like terms: 0 + -1 = -1
4t = -1

Divide each side by '4'.
t = -0.25

Simplifying
t = -0.25
Solution
t = {-0.4, -0.25}