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

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


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

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

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

Multiply (-7 + 2x) * (-2 + 7x)
(-7(-2 + 7x) + 2x * (-2 + 7x)) = 0
((-2 * -7 + 7x * -7) + 2x * (-2 + 7x)) = 0
((14 + -49x) + 2x * (-2 + 7x)) = 0
(14 + -49x + (-2 * 2x + 7x * 2x)) = 0
(14 + -49x + (-4x + 14x2)) = 0

Combine like terms: -49x + -4x = -53x
(14 + -53x + 14x2) = 0

Solving
14 + -53x + 14x2 = 0

Solving for variable 'x'.

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


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

Simplifying
2 + -7x = 0

Solving
2 + -7x = 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 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857

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

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {0.2857142857, 3.5}

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