(2x+3)(x+4)=x+24

Solution for (2x+3)(x+4)=x+24 equation:

Simplifying
(2x + 3)(x + 4) = x + 24

Reorder the terms:
(3 + 2x)(x + 4) = x + 24

Reorder the terms:
(3 + 2x)(4 + x) = x + 24

Multiply (3 + 2x) * (4 + x)
(3(4 + x) + 2x * (4 + x)) = x + 24
((4 * 3 + x * 3) + 2x * (4 + x)) = x + 24
((12 + 3x) + 2x * (4 + x)) = x + 24
(12 + 3x + (4 * 2x + x * 2x)) = x + 24
(12 + 3x + (8x + 2x2)) = x + 24

Combine like terms: 3x + 8x = 11x
(12 + 11x + 2x2) = x + 24

Reorder the terms:
12 + 11x + 2x2 = 24 + x

Solving
12 + 11x + 2x2 = 24 + x

Solving for variable 'x'.

Reorder the terms:
12 + -24 + 11x + -1x + 2x2 = 24 + x + -24 + -1x

Combine like terms: 12 + -24 = -12
-12 + 11x + -1x + 2x2 = 24 + x + -24 + -1x

Combine like terms: 11x + -1x = 10x
-12 + 10x + 2x2 = 24 + x + -24 + -1x

Reorder the terms:
-12 + 10x + 2x2 = 24 + -24 + x + -1x

Combine like terms: 24 + -24 = 0
-12 + 10x + 2x2 = 0 + x + -1x
-12 + 10x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-12 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 5x + x2) = 0

Factor a trinomial.
2((-6 + -1x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
x = {-6, 1}