(2x+3)(2x+1)=24

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Solution for (2x+3)(2x+1)=24 equation: 


Simplifying
(2x + 3)(2x + 1) = 24

Reorder the terms:
(3 + 2x)(2x + 1) = 24

Reorder the terms:
(3 + 2x)(1 + 2x) = 24

Multiply (3 + 2x) * (1 + 2x)
(3(1 + 2x) + 2x * (1 + 2x)) = 24
((1 * 3 + 2x * 3) + 2x * (1 + 2x)) = 24
((3 + 6x) + 2x * (1 + 2x)) = 24
(3 + 6x + (1 * 2x + 2x * 2x)) = 24
(3 + 6x + (2x + 4x2)) = 24

Combine like terms: 6x + 2x = 8x
(3 + 8x + 4x2) = 24

Solving
3 + 8x + 4x2 = 24

Solving for variable 'x'.

Reorder the terms:
3 + -24 + 8x + 4x2 = 24 + -24

Combine like terms: 3 + -24 = -21
-21 + 8x + 4x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-21 + 8x + 4x2 = 0

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


Subproblem 1
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

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 = {-3.5, 1.5}

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