=(x-6)(3x+7)

Solution for =(x-6)(3x+7) equation:

Simplifying
0 = (x + -6)(3x + 7)

Reorder the terms:
0 = (-6 + x)(3x + 7)

Reorder the terms:
0 = (-6 + x)(7 + 3x)

Multiply (-6 + x) * (7 + 3x)
0 = (-6(7 + 3x) + x(7 + 3x))
0 = ((7 * -6 + 3x * -6) + x(7 + 3x))
0 = ((-42 + -18x) + x(7 + 3x))
0 = (-42 + -18x + (7 * x + 3x * x))
0 = (-42 + -18x + (7x + 3x2))

Combine like terms: -18x + 7x = -11x
0 = (-42 + -11x + 3x2)

Solving
0 = -42 + -11x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 42 = 42
42 + 11x + -3x2 = -42 + -11x + 3x2 + 42 + 11x + -3x2

Reorder the terms:
42 + 11x + -3x2 = -42 + 42 + -11x + 11x + 3x2 + -3x2

Combine like terms: -42 + 42 = 0
42 + 11x + -3x2 = 0 + -11x + 11x + 3x2 + -3x2
42 + 11x + -3x2 = -11x + 11x + 3x2 + -3x2

Combine like terms: -11x + 11x = 0
42 + 11x + -3x2 = 0 + 3x2 + -3x2
42 + 11x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
42 + 11x + -3x2 = 0

Factor a trinomial.
(6 + -1x)(7 + 3x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 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 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333
Solution
x = {6, -2.333333333}