(4x-8)(x+5)=(5x-2)(x-2)

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Solution for (4x-8)(x+5)=(5x-2)(x-2) equation: 


Simplifying
(4x + -8)(x + 5) = (5x + -2)(x + -2)

Reorder the terms:
(-8 + 4x)(x + 5) = (5x + -2)(x + -2)

Reorder the terms:
(-8 + 4x)(5 + x) = (5x + -2)(x + -2)

Multiply (-8 + 4x) * (5 + x)
(-8(5 + x) + 4x * (5 + x)) = (5x + -2)(x + -2)
((5 * -8 + x * -8) + 4x * (5 + x)) = (5x + -2)(x + -2)
((-40 + -8x) + 4x * (5 + x)) = (5x + -2)(x + -2)
(-40 + -8x + (5 * 4x + x * 4x)) = (5x + -2)(x + -2)
(-40 + -8x + (20x + 4x2)) = (5x + -2)(x + -2)

Combine like terms: -8x + 20x = 12x
(-40 + 12x + 4x2) = (5x + -2)(x + -2)

Reorder the terms:
-40 + 12x + 4x2 = (-2 + 5x)(x + -2)

Reorder the terms:
-40 + 12x + 4x2 = (-2 + 5x)(-2 + x)

Multiply (-2 + 5x) * (-2 + x)
-40 + 12x + 4x2 = (-2(-2 + x) + 5x * (-2 + x))
-40 + 12x + 4x2 = ((-2 * -2 + x * -2) + 5x * (-2 + x))
-40 + 12x + 4x2 = ((4 + -2x) + 5x * (-2 + x))
-40 + 12x + 4x2 = (4 + -2x + (-2 * 5x + x * 5x))
-40 + 12x + 4x2 = (4 + -2x + (-10x + 5x2))

Combine like terms: -2x + -10x = -12x
-40 + 12x + 4x2 = (4 + -12x + 5x2)

Solving
-40 + 12x + 4x2 = 4 + -12x + 5x2

Solving for variable 'x'.

Reorder the terms:
-40 + -4 + 12x + 12x + 4x2 + -5x2 = 4 + -12x + 5x2 + -4 + 12x + -5x2

Combine like terms: -40 + -4 = -44
-44 + 12x + 12x + 4x2 + -5x2 = 4 + -12x + 5x2 + -4 + 12x + -5x2

Combine like terms: 12x + 12x = 24x
-44 + 24x + 4x2 + -5x2 = 4 + -12x + 5x2 + -4 + 12x + -5x2

Combine like terms: 4x2 + -5x2 = -1x2
-44 + 24x + -1x2 = 4 + -12x + 5x2 + -4 + 12x + -5x2

Reorder the terms:
-44 + 24x + -1x2 = 4 + -4 + -12x + 12x + 5x2 + -5x2

Combine like terms: 4 + -4 = 0
-44 + 24x + -1x2 = 0 + -12x + 12x + 5x2 + -5x2
-44 + 24x + -1x2 = -12x + 12x + 5x2 + -5x2

Combine like terms: -12x + 12x = 0
-44 + 24x + -1x2 = 0 + 5x2 + -5x2
-44 + 24x + -1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-44 + 24x + -1x2 = 0

Factor a trinomial.
(-22 + x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-22 + x)' equal to zero and attempt to solve:

Simplifying
-22 + x = 0

Solving
-22 + x = 0

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

Add '22' to each side of the equation.
-22 + 22 + x = 0 + 22

Combine like terms: -22 + 22 = 0
0 + x = 0 + 22
x = 0 + 22

Combine like terms: 0 + 22 = 22
x = 22

Simplifying
x = 22

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {22, 2}

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