14-(7-t)*(4+t)=2t

Solution for 14-(7-t)*(4+t)=2t equation:

Simplifying
14 + -1(7 + -1t)(4 + t) = 2t

Multiply (7 + -1t) * (4 + t)
14 + -1(7(4 + t) + -1t * (4 + t)) = 2t
14 + -1((4 * 7 + t * 7) + -1t * (4 + t)) = 2t
14 + -1((28 + 7t) + -1t * (4 + t)) = 2t
14 + -1(28 + 7t + (4 * -1t + t * -1t)) = 2t
14 + -1(28 + 7t + (-4t + -1t2)) = 2t

Combine like terms: 7t + -4t = 3t
14 + -1(28 + 3t + -1t2) = 2t
14 + (28 * -1 + 3t * -1 + -1t2 * -1) = 2t
14 + (-28 + -3t + 1t2) = 2t

Combine like terms: 14 + -28 = -14
-14 + -3t + 1t2 = 2t

Solving
-14 + -3t + 1t2 = 2t

Solving for variable 't'.

Reorder the terms:
-14 + -3t + -2t + 1t2 = 2t + -2t

Combine like terms: -3t + -2t = -5t
-14 + -5t + 1t2 = 2t + -2t

Combine like terms: 2t + -2t = 0
-14 + -5t + 1t2 = 0

Factor a trinomial.
(-2 + -1t)(7 + -1t) = 0

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

Simplifying
-2 + -1t = 0

Solving
-2 + -1t = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1t = 0 + 2
-1t = 0 + 2

Combine like terms: 0 + 2 = 2
-1t = 2

Divide each side by '-1'.
t = -2

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

Simplifying
7 + -1t = 0

Solving
7 + -1t = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1t = 0 + -7

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

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

Divide each side by '-1'.
t = 7

Simplifying
t = 7
Solution
t = {-2, 7}