(2x-5)(x+4)=(x+4)(x-2)

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Solution for (2x-5)(x+4)=(x+4)(x-2) equation: 


Simplifying
(2x + -5)(x + 4) = (x + 4)(x + -2)

Reorder the terms:
(-5 + 2x)(x + 4) = (x + 4)(x + -2)

Reorder the terms:
(-5 + 2x)(4 + x) = (x + 4)(x + -2)

Multiply (-5 + 2x) * (4 + x)
(-5(4 + x) + 2x * (4 + x)) = (x + 4)(x + -2)
((4 * -5 + x * -5) + 2x * (4 + x)) = (x + 4)(x + -2)
((-20 + -5x) + 2x * (4 + x)) = (x + 4)(x + -2)
(-20 + -5x + (4 * 2x + x * 2x)) = (x + 4)(x + -2)
(-20 + -5x + (8x + 2x2)) = (x + 4)(x + -2)

Combine like terms: -5x + 8x = 3x
(-20 + 3x + 2x2) = (x + 4)(x + -2)

Reorder the terms:
-20 + 3x + 2x2 = (4 + x)(x + -2)

Reorder the terms:
-20 + 3x + 2x2 = (4 + x)(-2 + x)

Multiply (4 + x) * (-2 + x)
-20 + 3x + 2x2 = (4(-2 + x) + x(-2 + x))
-20 + 3x + 2x2 = ((-2 * 4 + x * 4) + x(-2 + x))
-20 + 3x + 2x2 = ((-8 + 4x) + x(-2 + x))
-20 + 3x + 2x2 = (-8 + 4x + (-2 * x + x * x))
-20 + 3x + 2x2 = (-8 + 4x + (-2x + x2))

Combine like terms: 4x + -2x = 2x
-20 + 3x + 2x2 = (-8 + 2x + x2)

Solving
-20 + 3x + 2x2 = -8 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
-20 + 8 + 3x + -2x + 2x2 + -1x2 = -8 + 2x + x2 + 8 + -2x + -1x2

Combine like terms: -20 + 8 = -12
-12 + 3x + -2x + 2x2 + -1x2 = -8 + 2x + x2 + 8 + -2x + -1x2

Combine like terms: 3x + -2x = 1x
-12 + 1x + 2x2 + -1x2 = -8 + 2x + x2 + 8 + -2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-12 + 1x + 1x2 = -8 + 2x + x2 + 8 + -2x + -1x2

Reorder the terms:
-12 + 1x + 1x2 = -8 + 8 + 2x + -2x + x2 + -1x2

Combine like terms: -8 + 8 = 0
-12 + 1x + 1x2 = 0 + 2x + -2x + x2 + -1x2
-12 + 1x + 1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
-12 + 1x + 1x2 = 0 + x2 + -1x2
-12 + 1x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 1x + 1x2 = 0

Factor a trinomial.
(-4 + -1x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-4, 3}

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