(x-4)(x+3)=6(x+1)

Solution for (x-4)(x+3)=6(x+1) equation:

Simplifying
(x + -4)(x + 3) = 6(x + 1)

Reorder the terms:
(-4 + x)(x + 3) = 6(x + 1)

Reorder the terms:
(-4 + x)(3 + x) = 6(x + 1)

Multiply (-4 + x) * (3 + x)
(-4(3 + x) + x(3 + x)) = 6(x + 1)
((3 * -4 + x * -4) + x(3 + x)) = 6(x + 1)
((-12 + -4x) + x(3 + x)) = 6(x + 1)
(-12 + -4x + (3 * x + x * x)) = 6(x + 1)
(-12 + -4x + (3x + x2)) = 6(x + 1)

Combine like terms: -4x + 3x = -1x
(-12 + -1x + x2) = 6(x + 1)

Reorder the terms:
-12 + -1x + x2 = 6(1 + x)
-12 + -1x + x2 = (1 * 6 + x * 6)
-12 + -1x + x2 = (6 + 6x)

Solving
-12 + -1x + x2 = 6 + 6x

Solving for variable 'x'.

Reorder the terms:
-12 + -6 + -1x + -6x + x2 = 6 + 6x + -6 + -6x

Combine like terms: -12 + -6 = -18
-18 + -1x + -6x + x2 = 6 + 6x + -6 + -6x

Combine like terms: -1x + -6x = -7x
-18 + -7x + x2 = 6 + 6x + -6 + -6x

Reorder the terms:
-18 + -7x + x2 = 6 + -6 + 6x + -6x

Combine like terms: 6 + -6 = 0
-18 + -7x + x2 = 0 + 6x + -6x
-18 + -7x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-18 + -7x + x2 = 0

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

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 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 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-2, 9}