(x-7)(5x-100)=0

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Solution for (x-7)(5x-100)=0 equation: 


Simplifying
(x + -7)(5x + -100) = 0

Reorder the terms:
(-7 + x)(5x + -100) = 0

Reorder the terms:
(-7 + x)(-100 + 5x) = 0

Multiply (-7 + x) * (-100 + 5x)
(-7(-100 + 5x) + x(-100 + 5x)) = 0
((-100 * -7 + 5x * -7) + x(-100 + 5x)) = 0
((700 + -35x) + x(-100 + 5x)) = 0
(700 + -35x + (-100 * x + 5x * x)) = 0
(700 + -35x + (-100x + 5x2)) = 0

Combine like terms: -35x + -100x = -135x
(700 + -135x + 5x2) = 0

Solving
700 + -135x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(140 + -27x + x2) = 0

Factor a trinomial.
5((7 + -1x)(20 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
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

Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {7, 20}

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