(5+2x)(3+2x)=24

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Solution for (5+2x)(3+2x)=24 equation: 


Simplifying
(5 + 2x)(3 + 2x) = 24

Multiply (5 + 2x) * (3 + 2x)
(5(3 + 2x) + 2x * (3 + 2x)) = 24
((3 * 5 + 2x * 5) + 2x * (3 + 2x)) = 24
((15 + 10x) + 2x * (3 + 2x)) = 24
(15 + 10x + (3 * 2x + 2x * 2x)) = 24
(15 + 10x + (6x + 4x2)) = 24

Combine like terms: 10x + 6x = 16x
(15 + 16x + 4x2) = 24

Solving
15 + 16x + 4x2 = 24

Solving for variable 'x'.

Reorder the terms:
15 + -24 + 16x + 4x2 = 24 + -24

Combine like terms: 15 + -24 = -9
-9 + 16x + 4x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-9 + 16x + 4x2 = 0

Factor a trinomial.
(-9 + -2x)(1 + -2x) = 0


Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-4.5, 0.5}

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