(7x-28)(28x-7)=0

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Solution for (7x-28)(28x-7)=0 equation: 


Simplifying
(7x + -28)(28x + -7) = 0

Reorder the terms:
(-28 + 7x)(28x + -7) = 0

Reorder the terms:
(-28 + 7x)(-7 + 28x) = 0

Multiply (-28 + 7x) * (-7 + 28x)
(-28(-7 + 28x) + 7x * (-7 + 28x)) = 0
((-7 * -28 + 28x * -28) + 7x * (-7 + 28x)) = 0
((196 + -784x) + 7x * (-7 + 28x)) = 0
(196 + -784x + (-7 * 7x + 28x * 7x)) = 0
(196 + -784x + (-49x + 196x2)) = 0

Combine like terms: -784x + -49x = -833x
(196 + -833x + 196x2) = 0

Solving
196 + -833x + 196x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '49'.
49(4 + -17x + 4x2) = 0

Factor a trinomial.
49((1 + -4x)(4 + -1x)) = 0

Ignore the factor 49.

Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0.25, 4}

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