x(x+3)=(x-2)(x-4)

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Solution for x(x+3)=(x-2)(x-4) equation:


Simplifying
x(x + 3) = (x + -2)(x + -4)

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

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

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

Multiply (-2 + x) * (-4 + x)
3x + x2 = (-2(-4 + x) + x(-4 + x))
3x + x2 = ((-4 * -2 + x * -2) + x(-4 + x))
3x + x2 = ((8 + -2x) + x(-4 + x))
3x + x2 = (8 + -2x + (-4 * x + x * x))
3x + x2 = (8 + -2x + (-4x + x2))

Combine like terms: -2x + -4x = -6x
3x + x2 = (8 + -6x + x2)

Add '-1x2' to each side of the equation.
3x + x2 + -1x2 = 8 + -6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3x + 0 = 8 + -6x + x2 + -1x2
3x = 8 + -6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3x = 8 + -6x + 0
3x = 8 + -6x

Solving
3x = 8 + -6x

Solving for variable 'x'.

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

Add '6x' to each side of the equation.
3x + 6x = 8 + -6x + 6x

Combine like terms: 3x + 6x = 9x
9x = 8 + -6x + 6x

Combine like terms: -6x + 6x = 0
9x = 8 + 0
9x = 8

Divide each side by '9'.
x = 0.8888888889

Simplifying
x = 0.8888888889

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