(2x+3)(x-1)=6x

Solution for (2x+3)(x-1)=6x equation:

Simplifying
(2x + 3)(x + -1) = 6x

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

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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.5, 3}