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

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

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

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

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

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

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

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

Solving
-3 + -5x + 2x2 = 3 + 6x

Solving for variable 'x'.

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

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

Combine like terms: -5x + -6x = -11x
-6 + -11x + 2x2 = 3 + 6x + -3 + -6x

Reorder the terms:
-6 + -11x + 2x2 = 3 + -3 + 6x + -6x

Combine like terms: 3 + -3 = 0
-6 + -11x + 2x2 = 0 + 6x + -6x
-6 + -11x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-6 + -11x + 2x2 = 0

Factor a trinomial.
(-1 + -2x)(6 + -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 '(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 = {-0.5, 6}