t(7+t)=2(2t+5)

Solution for t(7+t)=2(2t+5) equation:

Simplifying
t(7 + t) = 2(2t + 5)
(7 * t + t * t) = 2(2t + 5)
(7t + t2) = 2(2t + 5)

Reorder the terms:
7t + t2 = 2(5 + 2t)
7t + t2 = (5 * 2 + 2t * 2)
7t + t2 = (10 + 4t)

Solving
7t + t2 = 10 + 4t

Solving for variable 't'.

Reorder the terms:
-10 + 7t + -4t + t2 = 10 + 4t + -10 + -4t

Combine like terms: 7t + -4t = 3t
-10 + 3t + t2 = 10 + 4t + -10 + -4t

Reorder the terms:
-10 + 3t + t2 = 10 + -10 + 4t + -4t

Combine like terms: 10 + -10 = 0
-10 + 3t + t2 = 0 + 4t + -4t
-10 + 3t + t2 = 4t + -4t

Combine like terms: 4t + -4t = 0
-10 + 3t + t2 = 0

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

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

Simplifying
-5 + -1t = 0

Solving
-5 + -1t = 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 + -1t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1t = 0 + 5
-1t = 0 + 5

Combine like terms: 0 + 5 = 5
-1t = 5

Divide each side by '-1'.
t = -5

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

Simplifying
2 + -1t = 0

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

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

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

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-5, 2}