(x-2)(x-7)=(x+1)(x-3)

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Solution for (x-2)(x-7)=(x+1)(x-3) equation: 


Simplifying
(x + -2)(x + -7) = (x + 1)(x + -3)

Reorder the terms:
(-2 + x)(x + -7) = (x + 1)(x + -3)

Reorder the terms:
(-2 + x)(-7 + x) = (x + 1)(x + -3)

Multiply (-2 + x) * (-7 + x)
(-2(-7 + x) + x(-7 + x)) = (x + 1)(x + -3)
((-7 * -2 + x * -2) + x(-7 + x)) = (x + 1)(x + -3)
((14 + -2x) + x(-7 + x)) = (x + 1)(x + -3)
(14 + -2x + (-7 * x + x * x)) = (x + 1)(x + -3)
(14 + -2x + (-7x + x2)) = (x + 1)(x + -3)

Combine like terms: -2x + -7x = -9x
(14 + -9x + x2) = (x + 1)(x + -3)

Reorder the terms:
14 + -9x + x2 = (1 + x)(x + -3)

Reorder the terms:
14 + -9x + x2 = (1 + x)(-3 + x)

Multiply (1 + x) * (-3 + x)
14 + -9x + x2 = (1(-3 + x) + x(-3 + x))
14 + -9x + x2 = ((-3 * 1 + x * 1) + x(-3 + x))
14 + -9x + x2 = ((-3 + 1x) + x(-3 + x))
14 + -9x + x2 = (-3 + 1x + (-3 * x + x * x))
14 + -9x + x2 = (-3 + 1x + (-3x + x2))

Combine like terms: 1x + -3x = -2x
14 + -9x + x2 = (-3 + -2x + x2)

Add '-1x2' to each side of the equation.
14 + -9x + x2 + -1x2 = -3 + -2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
14 + -9x + 0 = -3 + -2x + x2 + -1x2
14 + -9x = -3 + -2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
14 + -9x = -3 + -2x + 0
14 + -9x = -3 + -2x

Solving
14 + -9x = -3 + -2x

Solving for variable 'x'.

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

Add '2x' to each side of the equation.
14 + -9x + 2x = -3 + -2x + 2x

Combine like terms: -9x + 2x = -7x
14 + -7x = -3 + -2x + 2x

Combine like terms: -2x + 2x = 0
14 + -7x = -3 + 0
14 + -7x = -3

Add '-14' to each side of the equation.
14 + -14 + -7x = -3 + -14

Combine like terms: 14 + -14 = 0
0 + -7x = -3 + -14
-7x = -3 + -14

Combine like terms: -3 + -14 = -17
-7x = -17

Divide each side by '-7'.
x = 2.428571429

Simplifying
x = 2.428571429

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