(2x+3)(x+4)=33

Solution for (2x+3)(x+4)=33 equation:

Simplifying
(2x + 3)(x + 4) = 33

Reorder the terms:
(3 + 2x)(x + 4) = 33

Reorder the terms:
(3 + 2x)(4 + x) = 33

Multiply (3 + 2x) * (4 + x)
(3(4 + x) + 2x * (4 + x)) = 33
((4 * 3 + x * 3) + 2x * (4 + x)) = 33
((12 + 3x) + 2x * (4 + x)) = 33
(12 + 3x + (4 * 2x + x * 2x)) = 33
(12 + 3x + (8x + 2x2)) = 33

Combine like terms: 3x + 8x = 11x
(12 + 11x + 2x2) = 33

Solving
12 + 11x + 2x2 = 33

Solving for variable 'x'.

Reorder the terms:
12 + -33 + 11x + 2x2 = 33 + -33

Combine like terms: 12 + -33 = -21
-21 + 11x + 2x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-21 + 11x + 2x2 = 0

Factor a trinomial.
(-7 + -1x)(3 + -2x) = 0

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 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 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-7, 1.5}