(6x+7)(7x-9)=0

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Solution for (6x+7)(7x-9)=0 equation: 


Simplifying
(6x + 7)(7x + -9) = 0

Reorder the terms:
(7 + 6x)(7x + -9) = 0

Reorder the terms:
(7 + 6x)(-9 + 7x) = 0

Multiply (7 + 6x) * (-9 + 7x)
(7(-9 + 7x) + 6x * (-9 + 7x)) = 0
((-9 * 7 + 7x * 7) + 6x * (-9 + 7x)) = 0
((-63 + 49x) + 6x * (-9 + 7x)) = 0
(-63 + 49x + (-9 * 6x + 7x * 6x)) = 0
(-63 + 49x + (-54x + 42x2)) = 0

Combine like terms: 49x + -54x = -5x
(-63 + -5x + 42x2) = 0

Solving
-63 + -5x + 42x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -6x)(9 + -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 '(9 + -7x)' equal to zero and attempt to solve:

Simplifying
9 + -7x = 0

Solving
9 + -7x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -7x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -7x = 0 + -9
-7x = 0 + -9

Combine like terms: 0 + -9 = -9
-7x = -9

Divide each side by '-7'.
x = 1.285714286

Simplifying
x = 1.285714286
Solution
x = {-1.166666667, 1.285714286}

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