(x+3)(x-4)=(x-5)(x+2)

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Solution for (x+3)(x-4)=(x-5)(x+2) equation: 


Simplifying
(x + 3)(x + -4) = (x + -5)(x + 2)

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

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

Multiply (3 + x) * (-4 + x)
(3(-4 + x) + x(-4 + x)) = (x + -5)(x + 2)
((-4 * 3 + x * 3) + x(-4 + x)) = (x + -5)(x + 2)
((-12 + 3x) + x(-4 + x)) = (x + -5)(x + 2)
(-12 + 3x + (-4 * x + x * x)) = (x + -5)(x + 2)
(-12 + 3x + (-4x + x2)) = (x + -5)(x + 2)

Combine like terms: 3x + -4x = -1x
(-12 + -1x + x2) = (x + -5)(x + 2)

Reorder the terms:
-12 + -1x + x2 = (-5 + x)(x + 2)

Reorder the terms:
-12 + -1x + x2 = (-5 + x)(2 + x)

Multiply (-5 + x) * (2 + x)
-12 + -1x + x2 = (-5(2 + x) + x(2 + x))
-12 + -1x + x2 = ((2 * -5 + x * -5) + x(2 + x))
-12 + -1x + x2 = ((-10 + -5x) + x(2 + x))
-12 + -1x + x2 = (-10 + -5x + (2 * x + x * x))
-12 + -1x + x2 = (-10 + -5x + (2x + x2))

Combine like terms: -5x + 2x = -3x
-12 + -1x + x2 = (-10 + -3x + x2)

Add '-1x2' to each side of the equation.
-12 + -1x + x2 + -1x2 = -10 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + -1x + 0 = -10 + -3x + x2 + -1x2
-12 + -1x = -10 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + -1x = -10 + -3x + 0
-12 + -1x = -10 + -3x

Solving
-12 + -1x = -10 + -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 = -10 + -3x + 3x

Combine like terms: -1x + 3x = 2x
-12 + 2x = -10 + -3x + 3x

Combine like terms: -3x + 3x = 0
-12 + 2x = -10 + 0
-12 + 2x = -10

Add '12' to each side of the equation.
-12 + 12 + 2x = -10 + 12

Combine like terms: -12 + 12 = 0
0 + 2x = -10 + 12
2x = -10 + 12

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

Divide each side by '2'.
x = 1

Simplifying
x = 1

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