(6x-7)(6x+1)=0

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Solution for (6x-7)(6x+1)=0 equation: 


Simplifying
(6x + -7)(6x + 1) = 0

Reorder the terms:
(-7 + 6x)(6x + 1) = 0

Reorder the terms:
(-7 + 6x)(1 + 6x) = 0

Multiply (-7 + 6x) * (1 + 6x)
(-7(1 + 6x) + 6x * (1 + 6x)) = 0
((1 * -7 + 6x * -7) + 6x * (1 + 6x)) = 0
((-7 + -42x) + 6x * (1 + 6x)) = 0
(-7 + -42x + (1 * 6x + 6x * 6x)) = 0
(-7 + -42x + (6x + 36x2)) = 0

Combine like terms: -42x + 6x = -36x
(-7 + -36x + 36x2) = 0

Solving
-7 + -36x + 36x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-1 + -6x)' equal to zero and attempt to solve:

Simplifying
-1 + -6x = 0

Solving
-1 + -6x = 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 + -6x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6x = 0 + 1
-6x = 0 + 1

Combine like terms: 0 + 1 = 1
-6x = 1

Divide each side by '-6'.
x = -0.1666666667

Simplifying
x = -0.1666666667

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 = {-0.1666666667, 1.166666667}

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