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

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


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

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

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

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

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

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

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

Multiply (2 + x) * (-3 + x)
1 + -2x + x2 = (2(-3 + x) + x(-3 + x))
1 + -2x + x2 = ((-3 * 2 + x * 2) + x(-3 + x))
1 + -2x + x2 = ((-6 + 2x) + x(-3 + x))
1 + -2x + x2 = (-6 + 2x + (-3 * x + x * x))
1 + -2x + x2 = (-6 + 2x + (-3x + x2))

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

Add '-1x2' to each side of the equation.
1 + -2x + x2 + -1x2 = -6 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1 + -2x + 0 = -6 + -1x + x2 + -1x2
1 + -2x = -6 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1 + -2x = -6 + -1x + 0
1 + -2x = -6 + -1x

Solving
1 + -2x = -6 + -1x

Solving for variable 'x'.

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

Add 'x' to each side of the equation.
1 + -2x + x = -6 + -1x + x

Combine like terms: -2x + x = -1x
1 + -1x = -6 + -1x + x

Combine like terms: -1x + x = 0
1 + -1x = -6 + 0
1 + -1x = -6

Add '-1' to each side of the equation.
1 + -1 + -1x = -6 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = -6 + -1
-1x = -6 + -1

Combine like terms: -6 + -1 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

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