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

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


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

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

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

Multiply (4 + x) * (-3 + x)
(4(-3 + x) + x(-3 + x)) = (x + -2)(x + 1)
((-3 * 4 + x * 4) + x(-3 + x)) = (x + -2)(x + 1)
((-12 + 4x) + x(-3 + x)) = (x + -2)(x + 1)
(-12 + 4x + (-3 * x + x * x)) = (x + -2)(x + 1)
(-12 + 4x + (-3x + x2)) = (x + -2)(x + 1)

Combine like terms: 4x + -3x = 1x
(-12 + 1x + x2) = (x + -2)(x + 1)

Reorder the terms:
-12 + 1x + x2 = (-2 + x)(x + 1)

Reorder the terms:
-12 + 1x + x2 = (-2 + x)(1 + x)

Multiply (-2 + x) * (1 + x)
-12 + 1x + x2 = (-2(1 + x) + x(1 + x))
-12 + 1x + x2 = ((1 * -2 + x * -2) + x(1 + x))
-12 + 1x + x2 = ((-2 + -2x) + x(1 + x))
-12 + 1x + x2 = (-2 + -2x + (1 * x + x * x))
-12 + 1x + x2 = (-2 + -2x + (1x + x2))

Combine like terms: -2x + 1x = -1x
-12 + 1x + x2 = (-2 + -1x + x2)

Add '-1x2' to each side of the equation.
-12 + 1x + x2 + -1x2 = -2 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 1x + 0 = -2 + -1x + x2 + -1x2
-12 + 1x = -2 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 1x = -2 + -1x + 0
-12 + 1x = -2 + -1x

Solving
-12 + 1x = -2 + -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.
-12 + 1x + x = -2 + -1x + x

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

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

Add '12' to each side of the equation.
-12 + 12 + 2x = -2 + 12

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

Combine like terms: -2 + 12 = 10
2x = 10

Divide each side by '2'.
x = 5

Simplifying
x = 5

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