(7x-14)(5x+25)=0

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Solution for (7x-14)(5x+25)=0 equation: 


Simplifying
(7x + -14)(5x + 25) = 0

Reorder the terms:
(-14 + 7x)(5x + 25) = 0

Reorder the terms:
(-14 + 7x)(25 + 5x) = 0

Multiply (-14 + 7x) * (25 + 5x)
(-14(25 + 5x) + 7x * (25 + 5x)) = 0
((25 * -14 + 5x * -14) + 7x * (25 + 5x)) = 0
((-350 + -70x) + 7x * (25 + 5x)) = 0
(-350 + -70x + (25 * 7x + 5x * 7x)) = 0
(-350 + -70x + (175x + 35x2)) = 0

Combine like terms: -70x + 175x = 105x
(-350 + 105x + 35x2) = 0

Solving
-350 + 105x + 35x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '35'.
35(-10 + 3x + x2) = 0

Factor a trinomial.
35((-5 + -1x)(2 + -1x)) = 0

Ignore the factor 35.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-5, 2}

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