(5x-25)(7x+1)=0

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Solution for (5x-25)(7x+1)=0 equation: 


Simplifying
(5x + -25)(7x + 1) = 0

Reorder the terms:
(-25 + 5x)(7x + 1) = 0

Reorder the terms:
(-25 + 5x)(1 + 7x) = 0

Multiply (-25 + 5x) * (1 + 7x)
(-25(1 + 7x) + 5x * (1 + 7x)) = 0
((1 * -25 + 7x * -25) + 5x * (1 + 7x)) = 0
((-25 + -175x) + 5x * (1 + 7x)) = 0
(-25 + -175x + (1 * 5x + 7x * 5x)) = 0
(-25 + -175x + (5x + 35x2)) = 0

Combine like terms: -175x + 5x = -170x
(-25 + -170x + 35x2) = 0

Solving
-25 + -170x + 35x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + -34x + 7x2) = 0

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

Ignore the factor 5.

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

Simplifying
-1 + -7x = 0

Solving
-1 + -7x = 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 + -7x = 0 + 1

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

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

Divide each side by '-7'.
x = -0.1428571429

Simplifying
x = -0.1428571429

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-0.1428571429, 5}

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