x^2-7x+10=(x-5)(x-2)

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Solution for x^2-7x+10=(x-5)(x-2) equation: 


Simplifying
x2 + -7x + 10 = (x + -5)(x + -2)

Reorder the terms:
10 + -7x + x2 = (x + -5)(x + -2)

Reorder the terms:
10 + -7x + x2 = (-5 + x)(x + -2)

Reorder the terms:
10 + -7x + x2 = (-5 + x)(-2 + x)

Multiply (-5 + x) * (-2 + x)
10 + -7x + x2 = (-5(-2 + x) + x(-2 + x))
10 + -7x + x2 = ((-2 * -5 + x * -5) + x(-2 + x))
10 + -7x + x2 = ((10 + -5x) + x(-2 + x))
10 + -7x + x2 = (10 + -5x + (-2 * x + x * x))
10 + -7x + x2 = (10 + -5x + (-2x + x2))

Combine like terms: -5x + -2x = -7x
10 + -7x + x2 = (10 + -7x + x2)

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

Reorder the terms:
10 + -10 + -7x + x2 = 10 + -7x + -10 + x2

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

Reorder the terms:
-7x + x2 = 10 + -10 + -7x + x2

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

Add '7x' to each side of the equation.
-7x + 7x + x2 = -7x + 7x + x2

Combine like terms: -7x + 7x = 0
0 + x2 = -7x + 7x + x2
x2 = -7x + 7x + x2

Combine like terms: -7x + 7x = 0
x2 = 0 + x2
x2 = x2

Add '-1x2' to each side of the equation.
x2 + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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