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

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


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

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

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

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

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

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

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

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

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

Add '-1x2' to each side of the equation.
-12 + 1x + x2 + -1x2 = 2 + 3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 1x + 0 = 2 + 3x + x2 + -1x2
-12 + 1x = 2 + 3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 1x = 2 + 3x + 0
-12 + 1x = 2 + 3x

Solving
-12 + 1x = 2 + 3x

Solving for variable 'x'.

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

Add '-3x' to each side of the equation.
-12 + 1x + -3x = 2 + 3x + -3x

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

Combine like terms: 3x + -3x = 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 = 14
-2x = 14

Divide each side by '-2'.
x = -7

Simplifying
x = -7

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