(6x+7)(7x-12)=0

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Solution for (6x+7)(7x-12)=0 equation: 


Simplifying
(6x + 7)(7x + -12) = 0

Reorder the terms:
(7 + 6x)(7x + -12) = 0

Reorder the terms:
(7 + 6x)(-12 + 7x) = 0

Multiply (7 + 6x) * (-12 + 7x)
(7(-12 + 7x) + 6x * (-12 + 7x)) = 0
((-12 * 7 + 7x * 7) + 6x * (-12 + 7x)) = 0
((-84 + 49x) + 6x * (-12 + 7x)) = 0
(-84 + 49x + (-12 * 6x + 7x * 6x)) = 0
(-84 + 49x + (-72x + 42x2)) = 0

Combine like terms: 49x + -72x = -23x
(-84 + -23x + 42x2) = 0

Solving
-84 + -23x + 42x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -6x)(12 + -7x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(12 + -7x)' equal to zero and attempt to solve:

Simplifying
12 + -7x = 0

Solving
12 + -7x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -7x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -7x = 0 + -12
-7x = 0 + -12

Combine like terms: 0 + -12 = -12
-7x = -12

Divide each side by '-7'.
x = 1.714285714

Simplifying
x = 1.714285714
Solution
x = {-1.166666667, 1.714285714}

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