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

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

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

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

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

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

Combine like terms: -6x + 1x = -5x
(-3 + -5x + 2x2) = 4

Solving
-3 + -5x + 2x2 = 4

Solving for variable 'x'.

Reorder the terms:
-3 + -4 + -5x + 2x2 = 4 + -4

Combine like terms: -3 + -4 = -7
-7 + -5x + 2x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-7 + -5x + 2x2 = 0

Factor a trinomial.
(-1 + -1x)(7 + -2x) = 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 '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-1, 3.5}