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

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


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

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

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

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

Combine like terms: -3x + -1x = -4x
(3 + -4x + x2) + -1x(x + 2) = 7

Reorder the terms:
3 + -4x + x2 + -1x(2 + x) = 7
3 + -4x + x2 + (2 * -1x + x * -1x) = 7
3 + -4x + x2 + (-2x + -1x2) = 7

Reorder the terms:
3 + -4x + -2x + x2 + -1x2 = 7

Combine like terms: -4x + -2x = -6x
3 + -6x + x2 + -1x2 = 7

Combine like terms: x2 + -1x2 = 0
3 + -6x + 0 = 7
3 + -6x = 7

Solving
3 + -6x = 7

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + -6x = 7 + -3

Combine like terms: 3 + -3 = 0
0 + -6x = 7 + -3
-6x = 7 + -3

Combine like terms: 7 + -3 = 4
-6x = 4

Divide each side by '-6'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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