(2x+5)*(2x+5)-(2x+1)*(2x+1)=48

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Solution for (2x+5)*(2x+5)-(2x+1)*(2x+1)=48 equation: 


Simplifying
(2x + 5)(2x + 5) + -1(2x + 1)(2x + 1) = 48

Reorder the terms:
(5 + 2x)(2x + 5) + -1(2x + 1)(2x + 1) = 48

Reorder the terms:
(5 + 2x)(5 + 2x) + -1(2x + 1)(2x + 1) = 48

Multiply (5 + 2x) * (5 + 2x)
(5(5 + 2x) + 2x * (5 + 2x)) + -1(2x + 1)(2x + 1) = 48
((5 * 5 + 2x * 5) + 2x * (5 + 2x)) + -1(2x + 1)(2x + 1) = 48
((25 + 10x) + 2x * (5 + 2x)) + -1(2x + 1)(2x + 1) = 48
(25 + 10x + (5 * 2x + 2x * 2x)) + -1(2x + 1)(2x + 1) = 48
(25 + 10x + (10x + 4x2)) + -1(2x + 1)(2x + 1) = 48

Combine like terms: 10x + 10x = 20x
(25 + 20x + 4x2) + -1(2x + 1)(2x + 1) = 48

Reorder the terms:
25 + 20x + 4x2 + -1(1 + 2x)(2x + 1) = 48

Reorder the terms:
25 + 20x + 4x2 + -1(1 + 2x)(1 + 2x) = 48

Multiply (1 + 2x) * (1 + 2x)
25 + 20x + 4x2 + -1(1(1 + 2x) + 2x * (1 + 2x)) = 48
25 + 20x + 4x2 + -1((1 * 1 + 2x * 1) + 2x * (1 + 2x)) = 48
25 + 20x + 4x2 + -1((1 + 2x) + 2x * (1 + 2x)) = 48
25 + 20x + 4x2 + -1(1 + 2x + (1 * 2x + 2x * 2x)) = 48
25 + 20x + 4x2 + -1(1 + 2x + (2x + 4x2)) = 48

Combine like terms: 2x + 2x = 4x
25 + 20x + 4x2 + -1(1 + 4x + 4x2) = 48
25 + 20x + 4x2 + (1 * -1 + 4x * -1 + 4x2 * -1) = 48
25 + 20x + 4x2 + (-1 + -4x + -4x2) = 48

Reorder the terms:
25 + -1 + 20x + -4x + 4x2 + -4x2 = 48

Combine like terms: 25 + -1 = 24
24 + 20x + -4x + 4x2 + -4x2 = 48

Combine like terms: 20x + -4x = 16x
24 + 16x + 4x2 + -4x2 = 48

Combine like terms: 4x2 + -4x2 = 0
24 + 16x + 0 = 48
24 + 16x = 48

Solving
24 + 16x = 48

Solving for variable 'x'.

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

Add '-24' to each side of the equation.
24 + -24 + 16x = 48 + -24

Combine like terms: 24 + -24 = 0
0 + 16x = 48 + -24
16x = 48 + -24

Combine like terms: 48 + -24 = 24
16x = 24

Divide each side by '16'.
x = 1.5

Simplifying
x = 1.5

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