(x+5)(x-7)=(x-2)(x+4)

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Solution for (x+5)(x-7)=(x-2)(x+4) equation: 


Simplifying
(x + 5)(x + -7) = (x + -2)(x + 4)

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

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

Multiply (5 + x) * (-7 + x)
(5(-7 + x) + x(-7 + x)) = (x + -2)(x + 4)
((-7 * 5 + x * 5) + x(-7 + x)) = (x + -2)(x + 4)
((-35 + 5x) + x(-7 + x)) = (x + -2)(x + 4)
(-35 + 5x + (-7 * x + x * x)) = (x + -2)(x + 4)
(-35 + 5x + (-7x + x2)) = (x + -2)(x + 4)

Combine like terms: 5x + -7x = -2x
(-35 + -2x + x2) = (x + -2)(x + 4)

Reorder the terms:
-35 + -2x + x2 = (-2 + x)(x + 4)

Reorder the terms:
-35 + -2x + x2 = (-2 + x)(4 + x)

Multiply (-2 + x) * (4 + x)
-35 + -2x + x2 = (-2(4 + x) + x(4 + x))
-35 + -2x + x2 = ((4 * -2 + x * -2) + x(4 + x))
-35 + -2x + x2 = ((-8 + -2x) + x(4 + x))
-35 + -2x + x2 = (-8 + -2x + (4 * x + x * x))
-35 + -2x + x2 = (-8 + -2x + (4x + x2))

Combine like terms: -2x + 4x = 2x
-35 + -2x + x2 = (-8 + 2x + x2)

Add '-1x2' to each side of the equation.
-35 + -2x + x2 + -1x2 = -8 + 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-35 + -2x + 0 = -8 + 2x + x2 + -1x2
-35 + -2x = -8 + 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-35 + -2x = -8 + 2x + 0
-35 + -2x = -8 + 2x

Solving
-35 + -2x = -8 + 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.
-35 + -2x + -2x = -8 + 2x + -2x

Combine like terms: -2x + -2x = -4x
-35 + -4x = -8 + 2x + -2x

Combine like terms: 2x + -2x = 0
-35 + -4x = -8 + 0
-35 + -4x = -8

Add '35' to each side of the equation.
-35 + 35 + -4x = -8 + 35

Combine like terms: -35 + 35 = 0
0 + -4x = -8 + 35
-4x = -8 + 35

Combine like terms: -8 + 35 = 27
-4x = 27

Divide each side by '-4'.
x = -6.75

Simplifying
x = -6.75

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