(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 = 1
1 + 13t + -9t + -21t2 = -3 + 9t + 3 + -9t

Combine like terms: 13t + -9t = 4t
1 + 4t + -21t2 = -3 + 9t + 3 + -9t

Reorder the terms:
1 + 4t + -21t2 = -3 + 3 + 9t + -9t

Combine like terms: -3 + 3 = 0
1 + 4t + -21t2 = 0 + 9t + -9t
1 + 4t + -21t2 = 9t + -9t

Combine like terms: 9t + -9t = 0
1 + 4t + -21t2 = 0

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

Subproblem 1
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
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
Solution
t = {0.3333333333, -0.1428571429}