(x+8)(x-2)=53+(x-5)(x-3)

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Solution for (x+8)(x-2)=53+(x-5)(x-3) equation: 


Simplifying
(x + 8)(x + -2) = 53 + (x + -5)(x + -3)

Reorder the terms:
(8 + x)(x + -2) = 53 + (x + -5)(x + -3)

Reorder the terms:
(8 + x)(-2 + x) = 53 + (x + -5)(x + -3)

Multiply (8 + x) * (-2 + x)
(8(-2 + x) + x(-2 + x)) = 53 + (x + -5)(x + -3)
((-2 * 8 + x * 8) + x(-2 + x)) = 53 + (x + -5)(x + -3)
((-16 + 8x) + x(-2 + x)) = 53 + (x + -5)(x + -3)
(-16 + 8x + (-2 * x + x * x)) = 53 + (x + -5)(x + -3)
(-16 + 8x + (-2x + x2)) = 53 + (x + -5)(x + -3)

Combine like terms: 8x + -2x = 6x
(-16 + 6x + x2) = 53 + (x + -5)(x + -3)

Reorder the terms:
-16 + 6x + x2 = 53 + (-5 + x)(x + -3)

Reorder the terms:
-16 + 6x + x2 = 53 + (-5 + x)(-3 + x)

Multiply (-5 + x) * (-3 + x)
-16 + 6x + x2 = 53 + (-5(-3 + x) + x(-3 + x))
-16 + 6x + x2 = 53 + ((-3 * -5 + x * -5) + x(-3 + x))
-16 + 6x + x2 = 53 + ((15 + -5x) + x(-3 + x))
-16 + 6x + x2 = 53 + (15 + -5x + (-3 * x + x * x))
-16 + 6x + x2 = 53 + (15 + -5x + (-3x + x2))

Combine like terms: -5x + -3x = -8x
-16 + 6x + x2 = 53 + (15 + -8x + x2)

Combine like terms: 53 + 15 = 68
-16 + 6x + x2 = 68 + -8x + x2

Add '-1x2' to each side of the equation.
-16 + 6x + x2 + -1x2 = 68 + -8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-16 + 6x + 0 = 68 + -8x + x2 + -1x2
-16 + 6x = 68 + -8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-16 + 6x = 68 + -8x + 0
-16 + 6x = 68 + -8x

Solving
-16 + 6x = 68 + -8x

Solving for variable 'x'.

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

Add '8x' to each side of the equation.
-16 + 6x + 8x = 68 + -8x + 8x

Combine like terms: 6x + 8x = 14x
-16 + 14x = 68 + -8x + 8x

Combine like terms: -8x + 8x = 0
-16 + 14x = 68 + 0
-16 + 14x = 68

Add '16' to each side of the equation.
-16 + 16 + 14x = 68 + 16

Combine like terms: -16 + 16 = 0
0 + 14x = 68 + 16
14x = 68 + 16

Combine like terms: 68 + 16 = 84
14x = 84

Divide each side by '14'.
x = 6

Simplifying
x = 6

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