(6x+7)(7x-8)=0

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Solution for (6x+7)(7x-8)=0 equation: 


Simplifying
(6x + 7)(7x + -8) = 0

Reorder the terms:
(7 + 6x)(7x + -8) = 0

Reorder the terms:
(7 + 6x)(-8 + 7x) = 0

Multiply (7 + 6x) * (-8 + 7x)
(7(-8 + 7x) + 6x * (-8 + 7x)) = 0
((-8 * 7 + 7x * 7) + 6x * (-8 + 7x)) = 0
((-56 + 49x) + 6x * (-8 + 7x)) = 0
(-56 + 49x + (-8 * 6x + 7x * 6x)) = 0
(-56 + 49x + (-48x + 42x2)) = 0

Combine like terms: 49x + -48x = 1x
(-56 + 1x + 42x2) = 0

Solving
-56 + 1x + 42x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -6x)(8 + -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 '(8 + -7x)' equal to zero and attempt to solve:

Simplifying
8 + -7x = 0

Solving
8 + -7x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -7x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7x = 0 + -8
-7x = 0 + -8

Combine like terms: 0 + -8 = -8
-7x = -8

Divide each side by '-7'.
x = 1.142857143

Simplifying
x = 1.142857143
Solution
x = {-1.166666667, 1.142857143}

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