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

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

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

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

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

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

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

Solving
-6 + -1x + x2 = 4x

Solving for variable 'x'.

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

Combine like terms: -1x + -4x = -5x
-6 + -5x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-6 + -5x + x2 = 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}