(T-3)(2t-14)=

Solution for (T-3)(2t-14)= equation:

Simplifying
(T + -3)(2t + -14) = 0

Reorder the terms:
(-3 + T)(2t + -14) = 0

Reorder the terms:
(-3 + T)(-14 + 2t) = 0

Multiply (-3 + T) * (-14 + 2t)
(-3(-14 + 2t) + T(-14 + 2t)) = 0
((-14 * -3 + 2t * -3) + T(-14 + 2t)) = 0
((42 + -6t) + T(-14 + 2t)) = 0
(42 + -6t + (-14 * T + 2t * T)) = 0
(42 + -6t + (-14T + 2tT)) = 0

Reorder the terms:
(42 + -14T + -6t + 2tT) = 0
(42 + -14T + -6t + 2tT) = 0

Solving
42 + -14T + -6t + 2tT = 0

Solving for variable 'T'.

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

Add '-42' to each side of the equation.
42 + -14T + -6t + -42 + 2tT = 0 + -42

Reorder the terms:
42 + -42 + -14T + -6t + 2tT = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -14T + -6t + 2tT = 0 + -42
-14T + -6t + 2tT = 0 + -42

Combine like terms: 0 + -42 = -42
-14T + -6t + 2tT = -42

Add '6t' to each side of the equation.
-14T + -6t + 6t + 2tT = -42 + 6t

Combine like terms: -6t + 6t = 0
-14T + 0 + 2tT = -42 + 6t
-14T + 2tT = -42 + 6t

Reorder the terms:
42 + -14T + -6t + 2tT = -42 + 6t + 42 + -6t

Reorder the terms:
42 + -14T + -6t + 2tT = -42 + 42 + 6t + -6t

Combine like terms: -42 + 42 = 0
42 + -14T + -6t + 2tT = 0 + 6t + -6t
42 + -14T + -6t + 2tT = 6t + -6t

Combine like terms: 6t + -6t = 0
42 + -14T + -6t + 2tT = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -7T + -3t + tT) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(21 + -7T + -3t + tT)' equal to zero and attempt to solve:

Simplifying
21 + -7T + -3t + tT = 0

Solving
21 + -7T + -3t + tT = 0

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

Add '-21' to each side of the equation.
21 + -7T + -3t + -21 + tT = 0 + -21

Reorder the terms:
21 + -21 + -7T + -3t + tT = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -7T + -3t + tT = 0 + -21
-7T + -3t + tT = 0 + -21

Combine like terms: 0 + -21 = -21
-7T + -3t + tT = -21

Add '3t' to each side of the equation.
-7T + -3t + 3t + tT = -21 + 3t

Combine like terms: -3t + 3t = 0
-7T + 0 + tT = -21 + 3t
-7T + tT = -21 + 3t

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.