(7x-9)(2x+6)=0

Solution for (7x-9)(2x+6)=0 equation:

Simplifying
(7x + -9)(2x + 6) = 0

Reorder the terms:
(-9 + 7x)(2x + 6) = 0

Reorder the terms:
(-9 + 7x)(6 + 2x) = 0

Multiply (-9 + 7x) * (6 + 2x)
(-9(6 + 2x) + 7x * (6 + 2x)) = 0
((6 * -9 + 2x * -9) + 7x * (6 + 2x)) = 0
((-54 + -18x) + 7x * (6 + 2x)) = 0
(-54 + -18x + (6 * 7x + 2x * 7x)) = 0
(-54 + -18x + (42x + 14x2)) = 0

Combine like terms: -18x + 42x = 24x
(-54 + 24x + 14x2) = 0

Solving
-54 + 24x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + 12x + 7x2) = 0

Factor a trinomial.
2((-3 + -1x)(9 + -7x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
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 = {-3, 1.285714286}