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

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

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

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

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

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

Combine like terms: -35x + 14x = -21x
(-70 + -21x + 7x2) = 0

Solving
-70 + -21x + 7x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-10 + -3x + x2) = 0

Factor a trinomial.
7((-2 + -1x)(5 + -1x)) = 0

Ignore the factor 7.
Subproblem 1
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
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 = {-2, 5}