(x-4)(x+3)-3x=48

Solution for (x-4)(x+3)-3x=48 equation:

Simplifying
(x + -4)(x + 3) + -3x = 48

Reorder the terms:
(-4 + x)(x + 3) + -3x = 48

Reorder the terms:
(-4 + x)(3 + x) + -3x = 48

Multiply (-4 + x) * (3 + x)
(-4(3 + x) + x(3 + x)) + -3x = 48
((3 * -4 + x * -4) + x(3 + x)) + -3x = 48
((-12 + -4x) + x(3 + x)) + -3x = 48
(-12 + -4x + (3 * x + x * x)) + -3x = 48
(-12 + -4x + (3x + x2)) + -3x = 48

Combine like terms: -4x + 3x = -1x
(-12 + -1x + x2) + -3x = 48

Reorder the terms:
-12 + -1x + -3x + x2 = 48

Combine like terms: -1x + -3x = -4x
-12 + -4x + x2 = 48

Solving
-12 + -4x + x2 = 48

Solving for variable 'x'.

Reorder the terms:
-12 + -48 + -4x + x2 = 48 + -48

Combine like terms: -12 + -48 = -60
-60 + -4x + x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-60 + -4x + x2 = 0

Factor a trinomial.
(-6 + -1x)(10 + -1x) = 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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-6, 10}