(7x+14)(5-13x)=0

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Solution for (7x+14)(5-13x)=0 equation: 


Simplifying
(7x + 14)(5 + -13x) = 0

Reorder the terms:
(14 + 7x)(5 + -13x) = 0

Multiply (14 + 7x) * (5 + -13x)
(14(5 + -13x) + 7x * (5 + -13x)) = 0
((5 * 14 + -13x * 14) + 7x * (5 + -13x)) = 0
((70 + -182x) + 7x * (5 + -13x)) = 0
(70 + -182x + (5 * 7x + -13x * 7x)) = 0
(70 + -182x + (35x + -91x2)) = 0

Combine like terms: -182x + 35x = -147x
(70 + -147x + -91x2) = 0

Solving
70 + -147x + -91x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(10 + -21x + -13x2) = 0

Factor a trinomial.
7((5 + -13x)(2 + x)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(5 + -13x)' equal to zero and attempt to solve:

Simplifying
5 + -13x = 0

Solving
5 + -13x = 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 + -13x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -13x = 0 + -5
-13x = 0 + -5

Combine like terms: 0 + -5 = -5
-13x = -5

Divide each side by '-13'.
x = 0.3846153846

Simplifying
x = 0.3846153846

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {0.3846153846, -2}

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