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

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


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

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

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

Multiply (-2 + x) * (-7 + x)
(-2(-7 + x) + x(-7 + x)) = (x + -5)(x + 5)
((-7 * -2 + x * -2) + x(-7 + x)) = (x + -5)(x + 5)
((14 + -2x) + x(-7 + x)) = (x + -5)(x + 5)
(14 + -2x + (-7 * x + x * x)) = (x + -5)(x + 5)
(14 + -2x + (-7x + x2)) = (x + -5)(x + 5)

Combine like terms: -2x + -7x = -9x
(14 + -9x + x2) = (x + -5)(x + 5)

Reorder the terms:
14 + -9x + x2 = (-5 + x)(x + 5)

Reorder the terms:
14 + -9x + x2 = (-5 + x)(5 + x)

Multiply (-5 + x) * (5 + x)
14 + -9x + x2 = (-5(5 + x) + x(5 + x))
14 + -9x + x2 = ((5 * -5 + x * -5) + x(5 + x))
14 + -9x + x2 = ((-25 + -5x) + x(5 + x))
14 + -9x + x2 = (-25 + -5x + (5 * x + x * x))
14 + -9x + x2 = (-25 + -5x + (5x + x2))

Combine like terms: -5x + 5x = 0
14 + -9x + x2 = (-25 + 0 + x2)
14 + -9x + x2 = (-25 + x2)

Add '-1x2' to each side of the equation.
14 + -9x + x2 + -1x2 = -25 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
14 + -9x + 0 = -25 + x2 + -1x2
14 + -9x = -25 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
14 + -9x = -25 + 0
14 + -9x = -25

Solving
14 + -9x = -25

Solving for variable 'x'.

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

Add '-14' to each side of the equation.
14 + -14 + -9x = -25 + -14

Combine like terms: 14 + -14 = 0
0 + -9x = -25 + -14
-9x = -25 + -14

Combine like terms: -25 + -14 = -39
-9x = -39

Divide each side by '-9'.
x = 4.333333333

Simplifying
x = 4.333333333

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