(2X-3)(X+4)=13

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Solution for (2X-3)(X+4)=13 equation: 


Simplifying
(2X + -3)(X + 4) = 13

Reorder the terms:
(-3 + 2X)(X + 4) = 13

Reorder the terms:
(-3 + 2X)(4 + X) = 13

Multiply (-3 + 2X) * (4 + X)
(-3(4 + X) + 2X * (4 + X)) = 13
((4 * -3 + X * -3) + 2X * (4 + X)) = 13
((-12 + -3X) + 2X * (4 + X)) = 13
(-12 + -3X + (4 * 2X + X * 2X)) = 13
(-12 + -3X + (8X + 2X2)) = 13

Combine like terms: -3X + 8X = 5X
(-12 + 5X + 2X2) = 13

Solving
-12 + 5X + 2X2 = 13

Solving for variable 'X'.

Reorder the terms:
-12 + -13 + 5X + 2X2 = 13 + -13

Combine like terms: -12 + -13 = -25
-25 + 5X + 2X2 = 13 + -13

Combine like terms: 13 + -13 = 0
-25 + 5X + 2X2 = 0

Factor a trinomial.
(-5 + -1X)(5 + -2X) = 0


Subproblem 1
Set the factor '(-5 + -1X)' equal to zero and attempt to solve:

Simplifying
-5 + -1X = 0

Solving
-5 + -1X = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1X = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1X = 0 + 5
-1X = 0 + 5

Combine like terms: 0 + 5 = 5
-1X = 5

Divide each side by '-1'.
X = -5

Simplifying
X = -5

Subproblem 2
Set the factor '(5 + -2X)' equal to zero and attempt to solve:

Simplifying
5 + -2X = 0

Solving
5 + -2X = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2X = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2X = 0 + -5
-2X = 0 + -5

Combine like terms: 0 + -5 = -5
-2X = -5

Divide each side by '-2'.
X = 2.5

Simplifying
X = 2.5
Solution
X = {-5, 2.5}

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