5(7+2t)5(t+6)=

Solution for 5(7+2t)5(t+6)= equation:

Simplifying
5(7 + 2t) * 5(t + 6) = 0

Reorder the terms:
5(7 + 2t) * 5(6 + t) = 0

Reorder the terms for easier multiplication:
5 * 5(7 + 2t)(6 + t) = 0

Multiply 5 * 5
25(7 + 2t)(6 + t) = 0

Multiply (7 + 2t) * (6 + t)
25(7(6 + t) + 2t * (6 + t)) = 0
25((6 * 7 + t * 7) + 2t * (6 + t)) = 0
25((42 + 7t) + 2t * (6 + t)) = 0
25(42 + 7t + (6 * 2t + t * 2t)) = 0
25(42 + 7t + (12t + 2t2)) = 0

Combine like terms: 7t + 12t = 19t
25(42 + 19t + 2t2) = 0
(42 * 25 + 19t * 25 + 2t2 * 25) = 0
(1050 + 475t + 50t2) = 0

Solving
1050 + 475t + 50t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '25'.
25(42 + 19t + 2t2) = 0

Factor a trinomial.
25((6 + t)(7 + 2t)) = 0

Ignore the factor 25.
Subproblem 1
Set the factor '(6 + t)' equal to zero and attempt to solve:

Simplifying
6 + t = 0

Solving
6 + t = 0

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

Add '-6' to each side of the equation.
6 + -6 + t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + t = 0 + -6
t = 0 + -6

Combine like terms: 0 + -6 = -6
t = -6

Simplifying
t = -6
Subproblem 2
Set the factor '(7 + 2t)' equal to zero and attempt to solve:

Simplifying
7 + 2t = 0

Solving
7 + 2t = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2t = 0 + -7
2t = 0 + -7

Combine like terms: 0 + -7 = -7
2t = -7

Divide each side by '2'.
t = -3.5

Simplifying
t = -3.5
Solution
t = {-6, -3.5}