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

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


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

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

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

Multiply (-7 + 7x) * (7 + 5x)
(-7(7 + 5x) + 7x * (7 + 5x)) = 0
((7 * -7 + 5x * -7) + 7x * (7 + 5x)) = 0
((-49 + -35x) + 7x * (7 + 5x)) = 0
(-49 + -35x + (7 * 7x + 5x * 7x)) = 0
(-49 + -35x + (49x + 35x2)) = 0

Combine like terms: -35x + 49x = 14x
(-49 + 14x + 35x2) = 0

Solving
-49 + 14x + 35x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-7 + 2x + 5x2) = 0

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

Ignore the factor 7.

Subproblem 1
Set the factor '(-7 + -5x)' equal to zero and attempt to solve:

Simplifying
-7 + -5x = 0

Solving
-7 + -5x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -5x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5x = 0 + 7
-5x = 0 + 7

Combine like terms: 0 + 7 = 7
-5x = 7

Divide each side by '-5'.
x = -1.4

Simplifying
x = -1.4

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 = {-1.4, 1}

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