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

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


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

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

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

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

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

Solving
-70 + 35x + 35x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '35'.
35(-2 + x + x2) = 0

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

Ignore the factor 35.

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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-2, 1}

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