(x-2)(x+7)=(x-3)(x-4)

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Solution for (x-2)(x+7)=(x-3)(x-4) equation: 


Simplifying
(x + -2)(x + 7) = (x + -3)(x + -4)

Reorder the terms:
(-2 + x)(x + 7) = (x + -3)(x + -4)

Reorder the terms:
(-2 + x)(7 + x) = (x + -3)(x + -4)

Multiply (-2 + x) * (7 + x)
(-2(7 + x) + x(7 + x)) = (x + -3)(x + -4)
((7 * -2 + x * -2) + x(7 + x)) = (x + -3)(x + -4)
((-14 + -2x) + x(7 + x)) = (x + -3)(x + -4)
(-14 + -2x + (7 * x + x * x)) = (x + -3)(x + -4)
(-14 + -2x + (7x + x2)) = (x + -3)(x + -4)

Combine like terms: -2x + 7x = 5x
(-14 + 5x + x2) = (x + -3)(x + -4)

Reorder the terms:
-14 + 5x + x2 = (-3 + x)(x + -4)

Reorder the terms:
-14 + 5x + x2 = (-3 + x)(-4 + x)

Multiply (-3 + x) * (-4 + x)
-14 + 5x + x2 = (-3(-4 + x) + x(-4 + x))
-14 + 5x + x2 = ((-4 * -3 + x * -3) + x(-4 + x))
-14 + 5x + x2 = ((12 + -3x) + x(-4 + x))
-14 + 5x + x2 = (12 + -3x + (-4 * x + x * x))
-14 + 5x + x2 = (12 + -3x + (-4x + x2))

Combine like terms: -3x + -4x = -7x
-14 + 5x + x2 = (12 + -7x + x2)

Add '-1x2' to each side of the equation.
-14 + 5x + x2 + -1x2 = 12 + -7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-14 + 5x + 0 = 12 + -7x + x2 + -1x2
-14 + 5x = 12 + -7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-14 + 5x = 12 + -7x + 0
-14 + 5x = 12 + -7x

Solving
-14 + 5x = 12 + -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.
-14 + 5x + 7x = 12 + -7x + 7x

Combine like terms: 5x + 7x = 12x
-14 + 12x = 12 + -7x + 7x

Combine like terms: -7x + 7x = 0
-14 + 12x = 12 + 0
-14 + 12x = 12

Add '14' to each side of the equation.
-14 + 14 + 12x = 12 + 14

Combine like terms: -14 + 14 = 0
0 + 12x = 12 + 14
12x = 12 + 14

Combine like terms: 12 + 14 = 26
12x = 26

Divide each side by '12'.
x = 2.166666667

Simplifying
x = 2.166666667

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