(x-5)(x+3)=(x-7)(x+4)

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Solution for (x-5)(x+3)=(x-7)(x+4) equation: 


Simplifying
(x + -5)(x + 3) = (x + -7)(x + 4)

Reorder the terms:
(-5 + x)(x + 3) = (x + -7)(x + 4)

Reorder the terms:
(-5 + x)(3 + x) = (x + -7)(x + 4)

Multiply (-5 + x) * (3 + x)
(-5(3 + x) + x(3 + x)) = (x + -7)(x + 4)
((3 * -5 + x * -5) + x(3 + x)) = (x + -7)(x + 4)
((-15 + -5x) + x(3 + x)) = (x + -7)(x + 4)
(-15 + -5x + (3 * x + x * x)) = (x + -7)(x + 4)
(-15 + -5x + (3x + x2)) = (x + -7)(x + 4)

Combine like terms: -5x + 3x = -2x
(-15 + -2x + x2) = (x + -7)(x + 4)

Reorder the terms:
-15 + -2x + x2 = (-7 + x)(x + 4)

Reorder the terms:
-15 + -2x + x2 = (-7 + x)(4 + x)

Multiply (-7 + x) * (4 + x)
-15 + -2x + x2 = (-7(4 + x) + x(4 + x))
-15 + -2x + x2 = ((4 * -7 + x * -7) + x(4 + x))
-15 + -2x + x2 = ((-28 + -7x) + x(4 + x))
-15 + -2x + x2 = (-28 + -7x + (4 * x + x * x))
-15 + -2x + x2 = (-28 + -7x + (4x + x2))

Combine like terms: -7x + 4x = -3x
-15 + -2x + x2 = (-28 + -3x + x2)

Add '-1x2' to each side of the equation.
-15 + -2x + x2 + -1x2 = -28 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-15 + -2x + 0 = -28 + -3x + x2 + -1x2
-15 + -2x = -28 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-15 + -2x = -28 + -3x + 0
-15 + -2x = -28 + -3x

Solving
-15 + -2x = -28 + -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.
-15 + -2x + 3x = -28 + -3x + 3x

Combine like terms: -2x + 3x = 1x
-15 + 1x = -28 + -3x + 3x

Combine like terms: -3x + 3x = 0
-15 + 1x = -28 + 0
-15 + 1x = -28

Add '15' to each side of the equation.
-15 + 15 + 1x = -28 + 15

Combine like terms: -15 + 15 = 0
0 + 1x = -28 + 15
1x = -28 + 15

Combine like terms: -28 + 15 = -13
1x = -13

Divide each side by '1'.
x = -13

Simplifying
x = -13

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