3t(t+1)=4(t+1)

Solution for 3t(t+1)=4(t+1) equation:

Simplifying
3t(t + 1) = 4(t + 1)

Reorder the terms:
3t(1 + t) = 4(t + 1)
(1 * 3t + t * 3t) = 4(t + 1)
(3t + 3t2) = 4(t + 1)

Reorder the terms:
3t + 3t2 = 4(1 + t)
3t + 3t2 = (1 * 4 + t * 4)
3t + 3t2 = (4 + 4t)

Solving
3t + 3t2 = 4 + 4t

Solving for variable 't'.

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

Combine like terms: 3t + -4t = -1t
-4 + -1t + 3t2 = 4 + 4t + -4 + -4t

Reorder the terms:
-4 + -1t + 3t2 = 4 + -4 + 4t + -4t

Combine like terms: 4 + -4 = 0
-4 + -1t + 3t2 = 0 + 4t + -4t
-4 + -1t + 3t2 = 4t + -4t

Combine like terms: 4t + -4t = 0
-4 + -1t + 3t2 = 0

Factor a trinomial.
(-1 + -1t)(4 + -3t) = 0

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

Simplifying
-1 + -1t = 0

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

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

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

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

Simplifying
t = -1
Subproblem 2
Set the factor '(4 + -3t)' equal to zero and attempt to solve:

Simplifying
4 + -3t = 0

Solving
4 + -3t = 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 + -3t = 0 + -4

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

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

Divide each side by '-3'.
t = 1.333333333

Simplifying
t = 1.333333333
Solution
t = {-1, 1.333333333}