(T+4)(T+7)=54

Solution for (T+4)(T+7)=54 equation:

Simplifying
(T + 4)(T + 7) = 54

Reorder the terms:
(4 + T)(T + 7) = 54

Reorder the terms:
(4 + T)(7 + T) = 54

Multiply (4 + T) * (7 + T)
(4(7 + T) + T(7 + T)) = 54
((7 * 4 + T * 4) + T(7 + T)) = 54
((28 + 4T) + T(7 + T)) = 54
(28 + 4T + (7 * T + T * T)) = 54
(28 + 4T + (7T + T2)) = 54

Combine like terms: 4T + 7T = 11T
(28 + 11T + T2) = 54

Solving
28 + 11T + T2 = 54

Solving for variable 'T'.

Reorder the terms:
28 + -54 + 11T + T2 = 54 + -54

Combine like terms: 28 + -54 = -26
-26 + 11T + T2 = 54 + -54

Combine like terms: 54 + -54 = 0
-26 + 11T + T2 = 0

Factor a trinomial.
(-13 + -1T)(2 + -1T) = 0

Subproblem 1
Set the factor '(-13 + -1T)' equal to zero and attempt to solve:

Simplifying
-13 + -1T = 0

Solving
-13 + -1T = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1T = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1T = 0 + 13
-1T = 0 + 13

Combine like terms: 0 + 13 = 13
-1T = 13

Divide each side by '-1'.
T = -13

Simplifying
T = -13
Subproblem 2
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
Solution
T = {-13, 2}