x(x-3)=(x+3)(x-4)

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Solution for x(x-3)=(x+3)(x-4) equation:


Simplifying
x(x + -3) = (x + 3)(x + -4)

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

Reorder the terms:
-3x + x2 = (3 + x)(x + -4)

Reorder the terms:
-3x + x2 = (3 + x)(-4 + x)

Multiply (3 + x) * (-4 + x)
-3x + x2 = (3(-4 + x) + x(-4 + x))
-3x + x2 = ((-4 * 3 + x * 3) + x(-4 + x))
-3x + x2 = ((-12 + 3x) + x(-4 + x))
-3x + x2 = (-12 + 3x + (-4 * x + x * x))
-3x + x2 = (-12 + 3x + (-4x + x2))

Combine like terms: 3x + -4x = -1x
-3x + x2 = (-12 + -1x + x2)

Add '-1x2' to each side of the equation.
-3x + x2 + -1x2 = -12 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3x + 0 = -12 + -1x + x2 + -1x2
-3x = -12 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3x = -12 + -1x + 0
-3x = -12 + -1x

Solving
-3x = -12 + -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.
-3x + x = -12 + -1x + x

Combine like terms: -3x + x = -2x
-2x = -12 + -1x + x

Combine like terms: -1x + x = 0
-2x = -12 + 0
-2x = -12

Divide each side by '-2'.
x = 6

Simplifying
x = 6

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