3(x+1)(x-3)=x(2x-1)-3

Solution for 3(x+1)(x-3)=x(2x-1)-3 equation:

Simplifying
3(x + 1)(x + -3) = x(2x + -1) + -3

Reorder the terms:
3(1 + x)(x + -3) = x(2x + -1) + -3

Reorder the terms:
3(1 + x)(-3 + x) = x(2x + -1) + -3

Multiply (1 + x) * (-3 + x)
3(1(-3 + x) + x(-3 + x)) = x(2x + -1) + -3
3((-3 * 1 + x * 1) + x(-3 + x)) = x(2x + -1) + -3
3((-3 + 1x) + x(-3 + x)) = x(2x + -1) + -3
3(-3 + 1x + (-3 * x + x * x)) = x(2x + -1) + -3
3(-3 + 1x + (-3x + x2)) = x(2x + -1) + -3

Combine like terms: 1x + -3x = -2x
3(-3 + -2x + x2) = x(2x + -1) + -3
(-3 * 3 + -2x * 3 + x2 * 3) = x(2x + -1) + -3
(-9 + -6x + 3x2) = x(2x + -1) + -3

Reorder the terms:
-9 + -6x + 3x2 = x(-1 + 2x) + -3
-9 + -6x + 3x2 = (-1 * x + 2x * x) + -3
-9 + -6x + 3x2 = (-1x + 2x2) + -3

Reorder the terms:
-9 + -6x + 3x2 = -3 + -1x + 2x2

Solving
-9 + -6x + 3x2 = -3 + -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
-9 + 3 + -6x + x + 3x2 + -2x2 = -3 + -1x + 2x2 + 3 + x + -2x2

Combine like terms: -9 + 3 = -6
-6 + -6x + x + 3x2 + -2x2 = -3 + -1x + 2x2 + 3 + x + -2x2

Combine like terms: -6x + x = -5x
-6 + -5x + 3x2 + -2x2 = -3 + -1x + 2x2 + 3 + x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-6 + -5x + 1x2 = -3 + -1x + 2x2 + 3 + x + -2x2

Reorder the terms:
-6 + -5x + 1x2 = -3 + 3 + -1x + x + 2x2 + -2x2

Combine like terms: -3 + 3 = 0
-6 + -5x + 1x2 = 0 + -1x + x + 2x2 + -2x2
-6 + -5x + 1x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
-6 + -5x + 1x2 = 0 + 2x2 + -2x2
-6 + -5x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-6 + -5x + 1x2 = 0

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

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
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 = {-1, 6}