(2X+5)*(7-X)=24

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Solution for (2X+5)*(7-X)=24 equation: 


Simplifying
(2X + 5)(7 + -1X) = 24

Reorder the terms:
(5 + 2X)(7 + -1X) = 24

Multiply (5 + 2X) * (7 + -1X)
(5(7 + -1X) + 2X * (7 + -1X)) = 24
((7 * 5 + -1X * 5) + 2X * (7 + -1X)) = 24
((35 + -5X) + 2X * (7 + -1X)) = 24
(35 + -5X + (7 * 2X + -1X * 2X)) = 24
(35 + -5X + (14X + -2X2)) = 24

Combine like terms: -5X + 14X = 9X
(35 + 9X + -2X2) = 24

Solving
35 + 9X + -2X2 = 24

Solving for variable 'X'.

Reorder the terms:
35 + -24 + 9X + -2X2 = 24 + -24

Combine like terms: 35 + -24 = 11
11 + 9X + -2X2 = 24 + -24

Combine like terms: 24 + -24 = 0
11 + 9X + -2X2 = 0

Factor a trinomial.
(11 + -2X)(1 + X) = 0


Subproblem 1
Set the factor '(11 + -2X)' equal to zero and attempt to solve:

Simplifying
11 + -2X = 0

Solving
11 + -2X = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2X = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2X = 0 + -11
-2X = 0 + -11

Combine like terms: 0 + -11 = -11
-2X = -11

Divide each side by '-2'.
X = 5.5

Simplifying
X = 5.5

Subproblem 2
Set the factor '(1 + X)' equal to zero and attempt to solve:

Simplifying
1 + X = 0

Solving
1 + X = 0

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

Add '-1' to each side of the equation.
1 + -1 + X = 0 + -1

Combine like terms: 1 + -1 = 0
0 + X = 0 + -1
X = 0 + -1

Combine like terms: 0 + -1 = -1
X = -1

Simplifying
X = -1
Solution
X = {5.5, -1}

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