=(2x+3)(x+23)

Solution for =(2x+3)(x+23) equation:

Simplifying
0 = (2x + 3)(x + 23)

Reorder the terms:
0 = (3 + 2x)(x + 23)

Reorder the terms:
0 = (3 + 2x)(23 + x)

Multiply (3 + 2x) * (23 + x)
0 = (3(23 + x) + 2x * (23 + x))
0 = ((23 * 3 + x * 3) + 2x * (23 + x))
0 = ((69 + 3x) + 2x * (23 + x))
0 = (69 + 3x + (23 * 2x + x * 2x))
0 = (69 + 3x + (46x + 2x2))

Combine like terms: 3x + 46x = 49x
0 = (69 + 49x + 2x2)

Solving
0 = 69 + 49x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -69 = -69
-69 + -49x + -2x2 = 69 + 49x + 2x2 + -69 + -49x + -2x2

Reorder the terms:
-69 + -49x + -2x2 = 69 + -69 + 49x + -49x + 2x2 + -2x2

Combine like terms: 69 + -69 = 0
-69 + -49x + -2x2 = 0 + 49x + -49x + 2x2 + -2x2
-69 + -49x + -2x2 = 49x + -49x + 2x2 + -2x2

Combine like terms: 49x + -49x = 0
-69 + -49x + -2x2 = 0 + 2x2 + -2x2
-69 + -49x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-69 + -49x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(69 + 49x + 2x2) = 0

Factor a trinomial.
-1((23 + x)(3 + 2x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(23 + x)' equal to zero and attempt to solve:

Simplifying
23 + x = 0

Solving
23 + x = 0

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

Add '-23' to each side of the equation.
23 + -23 + x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + x = 0 + -23
x = 0 + -23

Combine like terms: 0 + -23 = -23
x = -23

Simplifying
x = -23
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 = {-23, -1.5}