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

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


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

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

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

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

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

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

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

Multiply (3 + x) * (3 + x)
-10 + -3x + x2 = (3(3 + x) + x(3 + x))
-10 + -3x + x2 = ((3 * 3 + x * 3) + x(3 + x))
-10 + -3x + x2 = ((9 + 3x) + x(3 + x))
-10 + -3x + x2 = (9 + 3x + (3 * x + x * x))
-10 + -3x + x2 = (9 + 3x + (3x + x2))

Combine like terms: 3x + 3x = 6x
-10 + -3x + x2 = (9 + 6x + x2)

Add '-1x2' to each side of the equation.
-10 + -3x + x2 + -1x2 = 9 + 6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + -3x + 0 = 9 + 6x + x2 + -1x2
-10 + -3x = 9 + 6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + -3x = 9 + 6x + 0
-10 + -3x = 9 + 6x

Solving
-10 + -3x = 9 + 6x

Solving for variable 'x'.

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

Add '-6x' to each side of the equation.
-10 + -3x + -6x = 9 + 6x + -6x

Combine like terms: -3x + -6x = -9x
-10 + -9x = 9 + 6x + -6x

Combine like terms: 6x + -6x = 0
-10 + -9x = 9 + 0
-10 + -9x = 9

Add '10' to each side of the equation.
-10 + 10 + -9x = 9 + 10

Combine like terms: -10 + 10 = 0
0 + -9x = 9 + 10
-9x = 9 + 10

Combine like terms: 9 + 10 = 19
-9x = 19

Divide each side by '-9'.
x = -2.111111111

Simplifying
x = -2.111111111

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