(x-3)(5-x)-2=(2-x)(x-4)+3

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Solution for (x-3)(5-x)-2=(2-x)(x-4)+3 equation:


Simplifying
(x + -3)(5 + -1x) + -2 = (2 + -1x)(x + -4) + 3

Reorder the terms:
(-3 + x)(5 + -1x) + -2 = (2 + -1x)(x + -4) + 3

Multiply (-3 + x) * (5 + -1x)
(-3(5 + -1x) + x(5 + -1x)) + -2 = (2 + -1x)(x + -4) + 3
((5 * -3 + -1x * -3) + x(5 + -1x)) + -2 = (2 + -1x)(x + -4) + 3
((-15 + 3x) + x(5 + -1x)) + -2 = (2 + -1x)(x + -4) + 3
(-15 + 3x + (5 * x + -1x * x)) + -2 = (2 + -1x)(x + -4) + 3
(-15 + 3x + (5x + -1x2)) + -2 = (2 + -1x)(x + -4) + 3

Combine like terms: 3x + 5x = 8x
(-15 + 8x + -1x2) + -2 = (2 + -1x)(x + -4) + 3

Reorder the terms:
-15 + -2 + 8x + -1x2 = (2 + -1x)(x + -4) + 3

Combine like terms: -15 + -2 = -17
-17 + 8x + -1x2 = (2 + -1x)(x + -4) + 3

Reorder the terms:
-17 + 8x + -1x2 = (2 + -1x)(-4 + x) + 3

Multiply (2 + -1x) * (-4 + x)
-17 + 8x + -1x2 = (2(-4 + x) + -1x * (-4 + x)) + 3
-17 + 8x + -1x2 = ((-4 * 2 + x * 2) + -1x * (-4 + x)) + 3
-17 + 8x + -1x2 = ((-8 + 2x) + -1x * (-4 + x)) + 3
-17 + 8x + -1x2 = (-8 + 2x + (-4 * -1x + x * -1x)) + 3
-17 + 8x + -1x2 = (-8 + 2x + (4x + -1x2)) + 3

Combine like terms: 2x + 4x = 6x
-17 + 8x + -1x2 = (-8 + 6x + -1x2) + 3

Reorder the terms:
-17 + 8x + -1x2 = -8 + 3 + 6x + -1x2

Combine like terms: -8 + 3 = -5
-17 + 8x + -1x2 = -5 + 6x + -1x2

Add 'x2' to each side of the equation.
-17 + 8x + -1x2 + x2 = -5 + 6x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-17 + 8x + 0 = -5 + 6x + -1x2 + x2
-17 + 8x = -5 + 6x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-17 + 8x = -5 + 6x + 0
-17 + 8x = -5 + 6x

Solving
-17 + 8x = -5 + 6x

Solving for variable 'x'.

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

Add '-6x' to each side of the equation.
-17 + 8x + -6x = -5 + 6x + -6x

Combine like terms: 8x + -6x = 2x
-17 + 2x = -5 + 6x + -6x

Combine like terms: 6x + -6x = 0
-17 + 2x = -5 + 0
-17 + 2x = -5

Add '17' to each side of the equation.
-17 + 17 + 2x = -5 + 17

Combine like terms: -17 + 17 = 0
0 + 2x = -5 + 17
2x = -5 + 17

Combine like terms: -5 + 17 = 12
2x = 12

Divide each side by '2'.
x = 6

Simplifying
x = 6

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