x(x-1)=x(2x-1)-18

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Solution for x(x-1)=x(2x-1)-18 equation: 


Simplifying
x(x + -1) = x(2x + -1) + -18

Reorder the terms:
x(-1 + x) = x(2x + -1) + -18
(-1 * x + x * x) = x(2x + -1) + -18
(-1x + x2) = x(2x + -1) + -18

Reorder the terms:
-1x + x2 = x(-1 + 2x) + -18
-1x + x2 = (-1 * x + 2x * x) + -18
-1x + x2 = (-1x + 2x2) + -18

Reorder the terms:
-1x + x2 = -18 + -1x + 2x2

Add 'x' to each side of the equation.
-1x + x + x2 = -18 + -1x + x + 2x2

Combine like terms: -1x + x = 0
0 + x2 = -18 + -1x + x + 2x2
x2 = -18 + -1x + x + 2x2

Combine like terms: -1x + x = 0
x2 = -18 + 0 + 2x2
x2 = -18 + 2x2

Solving
x2 = -18 + 2x2

Solving for variable 'x'.

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

Add '-2x2' to each side of the equation.
x2 + -2x2 = -18 + 2x2 + -2x2

Combine like terms: x2 + -2x2 = -1x2
-1x2 = -18 + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-1x2 = -18 + 0
-1x2 = -18

Divide each side by '-1'.
x2 = 18

Simplifying
x2 = 18

Take the square root of each side:
x = {-4.242640687, 4.242640687}

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