(x-7)(x+3)=(x-5)(x+2)

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Solution for (x-7)(x+3)=(x-5)(x+2) equation: 


Simplifying
(x + -7)(x + 3) = (x + -5)(x + 2)

Reorder the terms:
(-7 + x)(x + 3) = (x + -5)(x + 2)

Reorder the terms:
(-7 + x)(3 + x) = (x + -5)(x + 2)

Multiply (-7 + x) * (3 + x)
(-7(3 + x) + x(3 + x)) = (x + -5)(x + 2)
((3 * -7 + x * -7) + x(3 + x)) = (x + -5)(x + 2)
((-21 + -7x) + x(3 + x)) = (x + -5)(x + 2)
(-21 + -7x + (3 * x + x * x)) = (x + -5)(x + 2)
(-21 + -7x + (3x + x2)) = (x + -5)(x + 2)

Combine like terms: -7x + 3x = -4x
(-21 + -4x + x2) = (x + -5)(x + 2)

Reorder the terms:
-21 + -4x + x2 = (-5 + x)(x + 2)

Reorder the terms:
-21 + -4x + x2 = (-5 + x)(2 + x)

Multiply (-5 + x) * (2 + x)
-21 + -4x + x2 = (-5(2 + x) + x(2 + x))
-21 + -4x + x2 = ((2 * -5 + x * -5) + x(2 + x))
-21 + -4x + x2 = ((-10 + -5x) + x(2 + x))
-21 + -4x + x2 = (-10 + -5x + (2 * x + x * x))
-21 + -4x + x2 = (-10 + -5x + (2x + x2))

Combine like terms: -5x + 2x = -3x
-21 + -4x + x2 = (-10 + -3x + x2)

Add '-1x2' to each side of the equation.
-21 + -4x + x2 + -1x2 = -10 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-21 + -4x + 0 = -10 + -3x + x2 + -1x2
-21 + -4x = -10 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-21 + -4x = -10 + -3x + 0
-21 + -4x = -10 + -3x

Solving
-21 + -4x = -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.
-21 + -4x + 3x = -10 + -3x + 3x

Combine like terms: -4x + 3x = -1x
-21 + -1x = -10 + -3x + 3x

Combine like terms: -3x + 3x = 0
-21 + -1x = -10 + 0
-21 + -1x = -10

Add '21' to each side of the equation.
-21 + 21 + -1x = -10 + 21

Combine like terms: -21 + 21 = 0
0 + -1x = -10 + 21
-1x = -10 + 21

Combine like terms: -10 + 21 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11

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