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

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


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

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

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

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

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

Reorder the terms:
-10 + -3x + x2 = (5 + x)(x + -3)

Reorder the terms:
-10 + -3x + x2 = (5 + x)(-3 + x)

Multiply (5 + x) * (-3 + x)
-10 + -3x + x2 = (5(-3 + x) + x(-3 + x))
-10 + -3x + x2 = ((-3 * 5 + x * 5) + x(-3 + x))
-10 + -3x + x2 = ((-15 + 5x) + x(-3 + x))
-10 + -3x + x2 = (-15 + 5x + (-3 * x + x * x))
-10 + -3x + x2 = (-15 + 5x + (-3x + x2))

Combine like terms: 5x + -3x = 2x
-10 + -3x + x2 = (-15 + 2x + x2)

Add '-1x2' to each side of the equation.
-10 + -3x + x2 + -1x2 = -15 + 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + -3x + 0 = -15 + 2x + x2 + -1x2
-10 + -3x = -15 + 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + -3x = -15 + 2x + 0
-10 + -3x = -15 + 2x

Solving
-10 + -3x = -15 + 2x

Solving for variable 'x'.

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

Add '-2x' to each side of the equation.
-10 + -3x + -2x = -15 + 2x + -2x

Combine like terms: -3x + -2x = -5x
-10 + -5x = -15 + 2x + -2x

Combine like terms: 2x + -2x = 0
-10 + -5x = -15 + 0
-10 + -5x = -15

Add '10' to each side of the equation.
-10 + 10 + -5x = -15 + 10

Combine like terms: -10 + 10 = 0
0 + -5x = -15 + 10
-5x = -15 + 10

Combine like terms: -15 + 10 = -5
-5x = -5

Divide each side by '-5'.
x = 1

Simplifying
x = 1

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