(6x-7)(7x+7)=0

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Solution for (6x-7)(7x+7)=0 equation: 


Simplifying
(6x + -7)(7x + 7) = 0

Reorder the terms:
(-7 + 6x)(7x + 7) = 0

Reorder the terms:
(-7 + 6x)(7 + 7x) = 0

Multiply (-7 + 6x) * (7 + 7x)
(-7(7 + 7x) + 6x * (7 + 7x)) = 0
((7 * -7 + 7x * -7) + 6x * (7 + 7x)) = 0
((-49 + -49x) + 6x * (7 + 7x)) = 0
(-49 + -49x + (7 * 6x + 7x * 6x)) = 0
(-49 + -49x + (42x + 42x2)) = 0

Combine like terms: -49x + 42x = -7x
(-49 + -7x + 42x2) = 0

Solving
-49 + -7x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-7 + -1x + 6x2) = 0

Factor a trinomial.
7((-1 + -1x)(7 + -6x)) = 0

Ignore the factor 7.

Subproblem 1
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

Subproblem 2
Set the factor '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 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 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667
Solution
x = {-1, 1.166666667}

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