(2x+1)(x+3)=150

Solution for (2x+1)(x+3)=150 equation:

Simplifying
(2x + 1)(x + 3) = 150

Reorder the terms:
(1 + 2x)(x + 3) = 150

Reorder the terms:
(1 + 2x)(3 + x) = 150

Multiply (1 + 2x) * (3 + x)
(1(3 + x) + 2x * (3 + x)) = 150
((3 * 1 + x * 1) + 2x * (3 + x)) = 150
((3 + 1x) + 2x * (3 + x)) = 150
(3 + 1x + (3 * 2x + x * 2x)) = 150
(3 + 1x + (6x + 2x2)) = 150

Combine like terms: 1x + 6x = 7x
(3 + 7x + 2x2) = 150

Solving
3 + 7x + 2x2 = 150

Solving for variable 'x'.

Reorder the terms:
3 + -150 + 7x + 2x2 = 150 + -150

Combine like terms: 3 + -150 = -147
-147 + 7x + 2x2 = 150 + -150

Combine like terms: 150 + -150 = 0
-147 + 7x + 2x2 = 0

Factor a trinomial.
(-21 + -2x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-21 + -2x)' equal to zero and attempt to solve:

Simplifying
-21 + -2x = 0

Solving
-21 + -2x = 0

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

Add '21' to each side of the equation.
-21 + 21 + -2x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -2x = 0 + 21
-2x = 0 + 21

Combine like terms: 0 + 21 = 21
-2x = 21

Divide each side by '-2'.
x = -10.5

Simplifying
x = -10.5
Subproblem 2
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
Solution
x = {-10.5, 7}