(2x+1)2=4(x+2)2

Solution for (2x+1)2=4(x+2)2 equation:

Simplifying
(2x + 1) * 2 = 4(x + 2) * 2

Reorder the terms:
(1 + 2x) * 2 = 4(x + 2) * 2

Reorder the terms for easier multiplication:
2(1 + 2x) = 4(x + 2) * 2
(1 * 2 + 2x * 2) = 4(x + 2) * 2
(2 + 4x) = 4(x + 2) * 2

Reorder the terms:
2 + 4x = 4(2 + x) * 2

Reorder the terms for easier multiplication:
2 + 4x = 4 * 2(2 + x)

Multiply 4 * 2
2 + 4x = 8(2 + x)
2 + 4x = (2 * 8 + x * 8)
2 + 4x = (16 + 8x)

Solving
2 + 4x = 16 + 8x

Solving for variable 'x'.

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

Add '-8x' to each side of the equation.
2 + 4x + -8x = 16 + 8x + -8x

Combine like terms: 4x + -8x = -4x
2 + -4x = 16 + 8x + -8x

Combine like terms: 8x + -8x = 0
2 + -4x = 16 + 0
2 + -4x = 16

Add '-2' to each side of the equation.
2 + -2 + -4x = 16 + -2

Combine like terms: 2 + -2 = 0
0 + -4x = 16 + -2
-4x = 16 + -2

Combine like terms: 16 + -2 = 14
-4x = 14

Divide each side by '-4'.
x = -3.5

Simplifying
x = -3.5