(x+1)(x+4)=(x-2)(x-3)

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Solution for (x+1)(x+4)=(x-2)(x-3) equation: 


Simplifying
(x + 1)(x + 4) = (x + -2)(x + -3)

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

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

Multiply (1 + x) * (4 + x)
(1(4 + x) + x(4 + x)) = (x + -2)(x + -3)
((4 * 1 + x * 1) + x(4 + x)) = (x + -2)(x + -3)
((4 + 1x) + x(4 + x)) = (x + -2)(x + -3)
(4 + 1x + (4 * x + x * x)) = (x + -2)(x + -3)
(4 + 1x + (4x + x2)) = (x + -2)(x + -3)

Combine like terms: 1x + 4x = 5x
(4 + 5x + x2) = (x + -2)(x + -3)

Reorder the terms:
4 + 5x + x2 = (-2 + x)(x + -3)

Reorder the terms:
4 + 5x + x2 = (-2 + x)(-3 + x)

Multiply (-2 + x) * (-3 + x)
4 + 5x + x2 = (-2(-3 + x) + x(-3 + x))
4 + 5x + x2 = ((-3 * -2 + x * -2) + x(-3 + x))
4 + 5x + x2 = ((6 + -2x) + x(-3 + x))
4 + 5x + x2 = (6 + -2x + (-3 * x + x * x))
4 + 5x + x2 = (6 + -2x + (-3x + x2))

Combine like terms: -2x + -3x = -5x
4 + 5x + x2 = (6 + -5x + x2)

Add '-1x2' to each side of the equation.
4 + 5x + x2 + -1x2 = 6 + -5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + 5x + 0 = 6 + -5x + x2 + -1x2
4 + 5x = 6 + -5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + 5x = 6 + -5x + 0
4 + 5x = 6 + -5x

Solving
4 + 5x = 6 + -5x

Solving for variable 'x'.

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

Add '5x' to each side of the equation.
4 + 5x + 5x = 6 + -5x + 5x

Combine like terms: 5x + 5x = 10x
4 + 10x = 6 + -5x + 5x

Combine like terms: -5x + 5x = 0
4 + 10x = 6 + 0
4 + 10x = 6

Add '-4' to each side of the equation.
4 + -4 + 10x = 6 + -4

Combine like terms: 4 + -4 = 0
0 + 10x = 6 + -4
10x = 6 + -4

Combine like terms: 6 + -4 = 2
10x = 2

Divide each side by '10'.
x = 0.2

Simplifying
x = 0.2

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