(7t-2)(-3t+1)=3(1-3t)

Solution for (7t-2)(-3t+1)=3(1-3t) equation:

Simplifying
(7t + -2)(-3t + 1) = 3(1 + -3t)

Reorder the terms:
(-2 + 7t)(-3t + 1) = 3(1 + -3t)

Reorder the terms:
(-2 + 7t)(1 + -3t) = 3(1 + -3t)

Multiply (-2 + 7t) * (1 + -3t)
(-2(1 + -3t) + 7t * (1 + -3t)) = 3(1 + -3t)
((1 * -2 + -3t * -2) + 7t * (1 + -3t)) = 3(1 + -3t)
((-2 + 6t) + 7t * (1 + -3t)) = 3(1 + -3t)
(-2 + 6t + (1 * 7t + -3t * 7t)) = 3(1 + -3t)
(-2 + 6t + (7t + -21t2)) = 3(1 + -3t)

Combine like terms: 6t + 7t = 13t
(-2 + 13t + -21t2) = 3(1 + -3t)
-2 + 13t + -21t2 = (1 * 3 + -3t * 3)
-2 + 13t + -21t2 = (3 + -9t)

Solving
-2 + 13t + -21t2 = 3 + -9t

Solving for variable 't'.

Reorder the terms:
-2 + -3 + 13t + 9t + -21t2 = 3 + -9t + -3 + 9t

Combine like terms: -2 + -3 = -5
-5 + 13t + 9t + -21t2 = 3 + -9t + -3 + 9t

Combine like terms: 13t + 9t = 22t
-5 + 22t + -21t2 = 3 + -9t + -3 + 9t

Reorder the terms:
-5 + 22t + -21t2 = 3 + -3 + -9t + 9t

Combine like terms: 3 + -3 = 0
-5 + 22t + -21t2 = 0 + -9t + 9t
-5 + 22t + -21t2 = -9t + 9t

Combine like terms: -9t + 9t = 0
-5 + 22t + -21t2 = 0

Factor a trinomial.
(-5 + 7t)(1 + -3t) = 0

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

Simplifying
1 + -3t = 0

Solving
1 + -3t = 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 + -3t = 0 + -1

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

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

Divide each side by '-3'.
t = 0.3333333333

Simplifying
t = 0.3333333333
Solution
t = {0.7142857143, 0.3333333333}