(x-4)(6-x)=(x-3)(8-x)

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Solution for (x-4)(6-x)=(x-3)(8-x) equation: 


Simplifying
(x + -4)(6 + -1x) = (x + -3)(8 + -1x)

Reorder the terms:
(-4 + x)(6 + -1x) = (x + -3)(8 + -1x)

Multiply (-4 + x) * (6 + -1x)
(-4(6 + -1x) + x(6 + -1x)) = (x + -3)(8 + -1x)
((6 * -4 + -1x * -4) + x(6 + -1x)) = (x + -3)(8 + -1x)
((-24 + 4x) + x(6 + -1x)) = (x + -3)(8 + -1x)
(-24 + 4x + (6 * x + -1x * x)) = (x + -3)(8 + -1x)
(-24 + 4x + (6x + -1x2)) = (x + -3)(8 + -1x)

Combine like terms: 4x + 6x = 10x
(-24 + 10x + -1x2) = (x + -3)(8 + -1x)

Reorder the terms:
-24 + 10x + -1x2 = (-3 + x)(8 + -1x)

Multiply (-3 + x) * (8 + -1x)
-24 + 10x + -1x2 = (-3(8 + -1x) + x(8 + -1x))
-24 + 10x + -1x2 = ((8 * -3 + -1x * -3) + x(8 + -1x))
-24 + 10x + -1x2 = ((-24 + 3x) + x(8 + -1x))
-24 + 10x + -1x2 = (-24 + 3x + (8 * x + -1x * x))
-24 + 10x + -1x2 = (-24 + 3x + (8x + -1x2))

Combine like terms: 3x + 8x = 11x
-24 + 10x + -1x2 = (-24 + 11x + -1x2)

Add '24' to each side of the equation.
-24 + 10x + 24 + -1x2 = -24 + 11x + 24 + -1x2

Reorder the terms:
-24 + 24 + 10x + -1x2 = -24 + 11x + 24 + -1x2

Combine like terms: -24 + 24 = 0
0 + 10x + -1x2 = -24 + 11x + 24 + -1x2
10x + -1x2 = -24 + 11x + 24 + -1x2

Reorder the terms:
10x + -1x2 = -24 + 24 + 11x + -1x2

Combine like terms: -24 + 24 = 0
10x + -1x2 = 0 + 11x + -1x2
10x + -1x2 = 11x + -1x2

Add 'x2' to each side of the equation.
10x + -1x2 + x2 = 11x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
10x + 0 = 11x + -1x2 + x2
10x = 11x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
10x = 11x + 0
10x = 11x

Solving
10x = 11x

Solving for variable 'x'.

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

Add '-11x' to each side of the equation.
10x + -11x = 11x + -11x

Combine like terms: 10x + -11x = -1x
-1x = 11x + -11x

Combine like terms: 11x + -11x = 0
-1x = 0

Divide each side by '-1'.
x = 0

Simplifying
x = 0

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