0=(5+2t)(7+2t)(3+2t)

Solution for 0=(5+2t)(7+2t)(3+2t) equation:

Simplifying
0 = (5 + 2t)(7 + 2t)(3 + 2t)

Multiply (5 + 2t) * (7 + 2t)
0 = (5(7 + 2t) + 2t * (7 + 2t))(3 + 2t)
0 = ((7 * 5 + 2t * 5) + 2t * (7 + 2t))(3 + 2t)
0 = ((35 + 10t) + 2t * (7 + 2t))(3 + 2t)
0 = (35 + 10t + (7 * 2t + 2t * 2t))(3 + 2t)
0 = (35 + 10t + (14t + 4t2))(3 + 2t)

Combine like terms: 10t + 14t = 24t
0 = (35 + 24t + 4t2)(3 + 2t)

Multiply (35 + 24t + 4t2) * (3 + 2t)
0 = (35(3 + 2t) + 24t * (3 + 2t) + 4t2 * (3 + 2t))
0 = ((3 * 35 + 2t * 35) + 24t * (3 + 2t) + 4t2 * (3 + 2t))
0 = ((105 + 70t) + 24t * (3 + 2t) + 4t2 * (3 + 2t))
0 = (105 + 70t + (3 * 24t + 2t * 24t) + 4t2 * (3 + 2t))
0 = (105 + 70t + (72t + 48t2) + 4t2 * (3 + 2t))
0 = (105 + 70t + 72t + 48t2 + (3 * 4t2 + 2t * 4t2))
0 = (105 + 70t + 72t + 48t2 + (12t2 + 8t3))

Combine like terms: 70t + 72t = 142t
0 = (105 + 142t + 48t2 + 12t2 + 8t3)

Combine like terms: 48t2 + 12t2 = 60t2
0 = (105 + 142t + 60t2 + 8t3)

Solving
0 = 105 + 142t + 60t2 + 8t3

Solving for variable 't'.

Combine like terms: 0 + -105 = -105
-105 + -142t + -60t2 + -8t3 = 105 + 142t + 60t2 + 8t3 + -105 + -142t + -60t2 + -8t3

Reorder the terms:
-105 + -142t + -60t2 + -8t3 = 105 + -105 + 142t + -142t + 60t2 + -60t2 + 8t3 + -8t3

Combine like terms: 105 + -105 = 0
-105 + -142t + -60t2 + -8t3 = 0 + 142t + -142t + 60t2 + -60t2 + 8t3 + -8t3
-105 + -142t + -60t2 + -8t3 = 142t + -142t + 60t2 + -60t2 + 8t3 + -8t3

Combine like terms: 142t + -142t = 0
-105 + -142t + -60t2 + -8t3 = 0 + 60t2 + -60t2 + 8t3 + -8t3
-105 + -142t + -60t2 + -8t3 = 60t2 + -60t2 + 8t3 + -8t3

Combine like terms: 60t2 + -60t2 = 0
-105 + -142t + -60t2 + -8t3 = 0 + 8t3 + -8t3
-105 + -142t + -60t2 + -8t3 = 8t3 + -8t3

Combine like terms: 8t3 + -8t3 = 0
-105 + -142t + -60t2 + -8t3 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(105 + 142t + 60t2 + 8t3) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(105 + 142t + 60t2 + 8t3)' equal to zero and attempt to solve:

Simplifying
105 + 142t + 60t2 + 8t3 = 0

Solving
105 + 142t + 60t2 + 8t3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.