(x-2)(x+3)=(3x-4)(x-1)-4

Solution for (x-2)(x+3)=(3x-4)(x-1)-4 equation:

Simplifying
(x + -2)(x + 3) = (3x + -4)(x + -1) + -4

Reorder the terms:
(-2 + x)(x + 3) = (3x + -4)(x + -1) + -4

Reorder the terms:
(-2 + x)(3 + x) = (3x + -4)(x + -1) + -4

Multiply (-2 + x) * (3 + x)
(-2(3 + x) + x(3 + x)) = (3x + -4)(x + -1) + -4
((3 * -2 + x * -2) + x(3 + x)) = (3x + -4)(x + -1) + -4
((-6 + -2x) + x(3 + x)) = (3x + -4)(x + -1) + -4
(-6 + -2x + (3 * x + x * x)) = (3x + -4)(x + -1) + -4
(-6 + -2x + (3x + x2)) = (3x + -4)(x + -1) + -4

Combine like terms: -2x + 3x = 1x
(-6 + 1x + x2) = (3x + -4)(x + -1) + -4

Reorder the terms:
-6 + 1x + x2 = (-4 + 3x)(x + -1) + -4

Reorder the terms:
-6 + 1x + x2 = (-4 + 3x)(-1 + x) + -4

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

Combine like terms: -4x + -3x = -7x
-6 + 1x + x2 = (4 + -7x + 3x2) + -4

Reorder the terms:
-6 + 1x + x2 = 4 + -4 + -7x + 3x2

Combine like terms: 4 + -4 = 0
-6 + 1x + x2 = 0 + -7x + 3x2
-6 + 1x + x2 = -7x + 3x2

Solving
-6 + 1x + x2 = -7x + 3x2

Solving for variable 'x'.

Reorder the terms:
-6 + 1x + 7x + x2 + -3x2 = -7x + 3x2 + 7x + -3x2

Combine like terms: 1x + 7x = 8x
-6 + 8x + x2 + -3x2 = -7x + 3x2 + 7x + -3x2

Combine like terms: x2 + -3x2 = -2x2
-6 + 8x + -2x2 = -7x + 3x2 + 7x + -3x2

Reorder the terms:
-6 + 8x + -2x2 = -7x + 7x + 3x2 + -3x2

Combine like terms: -7x + 7x = 0
-6 + 8x + -2x2 = 0 + 3x2 + -3x2
-6 + 8x + -2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-6 + 8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 4x + -1x2) = 0

Factor a trinomial.
2((-3 + x)(1 + -1x)) = 0

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

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

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

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

Simplifying
x = 3
Subproblem 2
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
Solution
x = {3, 1}