(x-6)(7x+49)=0

Solution for (x-6)(7x+49)=0 equation:

Simplifying
(x + -6)(7x + 49) = 0

Reorder the terms:
(-6 + x)(7x + 49) = 0

Reorder the terms:
(-6 + x)(49 + 7x) = 0

Multiply (-6 + x) * (49 + 7x)
(-6(49 + 7x) + x(49 + 7x)) = 0
((49 * -6 + 7x * -6) + x(49 + 7x)) = 0
((-294 + -42x) + x(49 + 7x)) = 0
(-294 + -42x + (49 * x + 7x * x)) = 0
(-294 + -42x + (49x + 7x2)) = 0

Combine like terms: -42x + 49x = 7x
(-294 + 7x + 7x2) = 0

Solving
-294 + 7x + 7x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-42 + x + x2) = 0

Factor a trinomial.
7((-7 + -1x)(6 + -1x)) = 0

Ignore the factor 7.
Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-7, 6}