(x-2)(x-7)=0

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Solution for (x-2)(x-7)=0 equation:


Simplifying
(x + -2)(x + -7) = 0

Reorder the terms:
(-2 + x)(x + -7) = 0

Reorder the terms:
(-2 + x)(-7 + x) = 0

Multiply (-2 + x) * (-7 + x)
(-2(-7 + x) + x(-7 + x)) = 0
((-7 * -2 + x * -2) + x(-7 + x)) = 0
((14 + -2x) + x(-7 + x)) = 0
(14 + -2x + (-7 * x + x * x)) = 0
(14 + -2x + (-7x + x2)) = 0

Combine like terms: -2x + -7x = -9x
(14 + -9x + x2) = 0

Solving
14 + -9x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {2, 7}

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