(x-5)(x+2)=(x-3)(x+6)

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Solution for (x-5)(x+2)=(x-3)(x+6) equation: 


Simplifying
(x + -5)(x + 2) = (x + -3)(x + 6)

Reorder the terms:
(-5 + x)(x + 2) = (x + -3)(x + 6)

Reorder the terms:
(-5 + x)(2 + x) = (x + -3)(x + 6)

Multiply (-5 + x) * (2 + x)
(-5(2 + x) + x(2 + x)) = (x + -3)(x + 6)
((2 * -5 + x * -5) + x(2 + x)) = (x + -3)(x + 6)
((-10 + -5x) + x(2 + x)) = (x + -3)(x + 6)
(-10 + -5x + (2 * x + x * x)) = (x + -3)(x + 6)
(-10 + -5x + (2x + x2)) = (x + -3)(x + 6)

Combine like terms: -5x + 2x = -3x
(-10 + -3x + x2) = (x + -3)(x + 6)

Reorder the terms:
-10 + -3x + x2 = (-3 + x)(x + 6)

Reorder the terms:
-10 + -3x + x2 = (-3 + x)(6 + x)

Multiply (-3 + x) * (6 + x)
-10 + -3x + x2 = (-3(6 + x) + x(6 + x))
-10 + -3x + x2 = ((6 * -3 + x * -3) + x(6 + x))
-10 + -3x + x2 = ((-18 + -3x) + x(6 + x))
-10 + -3x + x2 = (-18 + -3x + (6 * x + x * x))
-10 + -3x + x2 = (-18 + -3x + (6x + x2))

Combine like terms: -3x + 6x = 3x
-10 + -3x + x2 = (-18 + 3x + x2)

Add '-1x2' to each side of the equation.
-10 + -3x + x2 + -1x2 = -18 + 3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + -3x + 0 = -18 + 3x + x2 + -1x2
-10 + -3x = -18 + 3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + -3x = -18 + 3x + 0
-10 + -3x = -18 + 3x

Solving
-10 + -3x = -18 + 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.
-10 + -3x + -3x = -18 + 3x + -3x

Combine like terms: -3x + -3x = -6x
-10 + -6x = -18 + 3x + -3x

Combine like terms: 3x + -3x = 0
-10 + -6x = -18 + 0
-10 + -6x = -18

Add '10' to each side of the equation.
-10 + 10 + -6x = -18 + 10

Combine like terms: -10 + 10 = 0
0 + -6x = -18 + 10
-6x = -18 + 10

Combine like terms: -18 + 10 = -8
-6x = -8

Divide each side by '-6'.
x = 1.333333333

Simplifying
x = 1.333333333

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