10t(t+4)=7t-20

Solution for 10t(t+4)=7t-20 equation:

Simplifying
10t(t + 4) = 7t + -20

Reorder the terms:
10t(4 + t) = 7t + -20
(4 * 10t + t * 10t) = 7t + -20
(40t + 10t2) = 7t + -20

Reorder the terms:
40t + 10t2 = -20 + 7t

Solving
40t + 10t2 = -20 + 7t

Solving for variable 't'.

Reorder the terms:
20 + 40t + -7t + 10t2 = -20 + 7t + 20 + -7t

Combine like terms: 40t + -7t = 33t
20 + 33t + 10t2 = -20 + 7t + 20 + -7t

Reorder the terms:
20 + 33t + 10t2 = -20 + 20 + 7t + -7t

Combine like terms: -20 + 20 = 0
20 + 33t + 10t2 = 0 + 7t + -7t
20 + 33t + 10t2 = 7t + -7t

Combine like terms: 7t + -7t = 0
20 + 33t + 10t2 = 0

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

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

Simplifying
5 + 2t = 0

Solving
5 + 2t = 0

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

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

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

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

Divide each side by '2'.
t = -2.5

Simplifying
t = -2.5
Subproblem 2
Set the factor '(4 + 5t)' equal to zero and attempt to solve:

Simplifying
4 + 5t = 0

Solving
4 + 5t = 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 + 5t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5t = 0 + -4
5t = 0 + -4

Combine like terms: 0 + -4 = -4
5t = -4

Divide each side by '5'.
t = -0.8

Simplifying
t = -0.8
Solution
t = {-2.5, -0.8}