(3x-6)(x+1)=462

Solution for (3x-6)(x+1)=462 equation:

Simplifying
(3x + -6)(x + 1) = 462

Reorder the terms:
(-6 + 3x)(x + 1) = 462

Reorder the terms:
(-6 + 3x)(1 + x) = 462

Multiply (-6 + 3x) * (1 + x)
(-6(1 + x) + 3x * (1 + x)) = 462
((1 * -6 + x * -6) + 3x * (1 + x)) = 462
((-6 + -6x) + 3x * (1 + x)) = 462
(-6 + -6x + (1 * 3x + x * 3x)) = 462
(-6 + -6x + (3x + 3x2)) = 462

Combine like terms: -6x + 3x = -3x
(-6 + -3x + 3x2) = 462

Solving
-6 + -3x + 3x2 = 462

Solving for variable 'x'.

Reorder the terms:
-6 + -462 + -3x + 3x2 = 462 + -462

Combine like terms: -6 + -462 = -468
-468 + -3x + 3x2 = 462 + -462

Combine like terms: 462 + -462 = 0
-468 + -3x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-156 + -1x + x2) = 0

Factor a trinomial.
3((-12 + -1x)(13 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {-12, 13}