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

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

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

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

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

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

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

Solving
-42 + 5x + 63x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -7x)(7 + -9x) = 0

Subproblem 1
Set the factor '(-6 + -7x)' equal to zero and attempt to solve:

Simplifying
-6 + -7x = 0

Solving
-6 + -7x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -7x = 0 + 6

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

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

Divide each side by '-7'.
x = -0.8571428571

Simplifying
x = -0.8571428571
Subproblem 2
Set the factor '(7 + -9x)' equal to zero and attempt to solve:

Simplifying
7 + -9x = 0

Solving
7 + -9x = 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 + -9x = 0 + -7

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

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

Divide each side by '-9'.
x = 0.7777777778

Simplifying
x = 0.7777777778
Solution
x = {-0.8571428571, 0.7777777778}