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

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

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

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

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

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

Combine like terms: -14x + 6x = -8x
(-42 + -8x + 2x2) = 0

Solving
-42 + -8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -4x + x2) = 0

Factor a trinomial.
2((-3 + -1x)(7 + -1x)) = 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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-3, 7}