49t^3+5t=42t^2

Solution for 49t^3+5t=42t^2 equation:

Simplifying
49t3 + 5t = 42t2

Reorder the terms:
5t + 49t3 = 42t2

Solving
5t + 49t3 = 42t2

Solving for variable 't'.

Reorder the terms:
5t + -42t2 + 49t3 = 42t2 + -42t2

Combine like terms: 42t2 + -42t2 = 0
5t + -42t2 + 49t3 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(5 + -42t + 49t2) = 0

Factor a trinomial.
t((1 + -7t)(5 + -7t)) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(1 + -7t)' equal to zero and attempt to solve:

Simplifying
1 + -7t = 0

Solving
1 + -7t = 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 + -7t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7t = 0 + -1
-7t = 0 + -1

Combine like terms: 0 + -1 = -1
-7t = -1

Divide each side by '-7'.
t = 0.1428571429

Simplifying
t = 0.1428571429
Subproblem 3
Set the factor '(5 + -7t)' equal to zero and attempt to solve:

Simplifying
5 + -7t = 0

Solving
5 + -7t = 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 + -7t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7t = 0 + -5
-7t = 0 + -5

Combine like terms: 0 + -5 = -5
-7t = -5

Divide each side by '-7'.
t = 0.7142857143

Simplifying
t = 0.7142857143
Solution
t = {0, 0.1428571429, 0.7142857143}