(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 = 7x
-21 + 4x + x2 = (10 + 7x + x2)

Add '-1x2' to each side of the equation.
-21 + 4x + x2 + -1x2 = 10 + 7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-21 + 4x + 0 = 10 + 7x + x2 + -1x2
-21 + 4x = 10 + 7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-21 + 4x = 10 + 7x + 0
-21 + 4x = 10 + 7x

Solving
-21 + 4x = 10 + 7x

Solving for variable 'x'.

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

Add '-7x' to each side of the equation.
-21 + 4x + -7x = 10 + 7x + -7x

Combine like terms: 4x + -7x = -3x
-21 + -3x = 10 + 7x + -7x

Combine like terms: 7x + -7x = 0
-21 + -3x = 10 + 0
-21 + -3x = 10

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

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

Combine like terms: 10 + 21 = 31
-3x = 31

Divide each side by '-3'.
x = -10.33333333

Simplifying
x = -10.33333333

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