(2x+3)(2x-3)+7=4(x+2)(x-2)+2x

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Solution for (2x+3)(2x-3)+7=4(x+2)(x-2)+2x equation: 


Simplifying
(2x + 3)(2x + -3) + 7 = 4(x + 2)(x + -2) + 2x

Reorder the terms:
(3 + 2x)(2x + -3) + 7 = 4(x + 2)(x + -2) + 2x

Reorder the terms:
(3 + 2x)(-3 + 2x) + 7 = 4(x + 2)(x + -2) + 2x

Multiply (3 + 2x) * (-3 + 2x)
(3(-3 + 2x) + 2x * (-3 + 2x)) + 7 = 4(x + 2)(x + -2) + 2x
((-3 * 3 + 2x * 3) + 2x * (-3 + 2x)) + 7 = 4(x + 2)(x + -2) + 2x
((-9 + 6x) + 2x * (-3 + 2x)) + 7 = 4(x + 2)(x + -2) + 2x
(-9 + 6x + (-3 * 2x + 2x * 2x)) + 7 = 4(x + 2)(x + -2) + 2x
(-9 + 6x + (-6x + 4x2)) + 7 = 4(x + 2)(x + -2) + 2x

Combine like terms: 6x + -6x = 0
(-9 + 0 + 4x2) + 7 = 4(x + 2)(x + -2) + 2x
(-9 + 4x2) + 7 = 4(x + 2)(x + -2) + 2x

Reorder the terms:
-9 + 7 + 4x2 = 4(x + 2)(x + -2) + 2x

Combine like terms: -9 + 7 = -2
-2 + 4x2 = 4(x + 2)(x + -2) + 2x

Reorder the terms:
-2 + 4x2 = 4(2 + x)(x + -2) + 2x

Reorder the terms:
-2 + 4x2 = 4(2 + x)(-2 + x) + 2x

Multiply (2 + x) * (-2 + x)
-2 + 4x2 = 4(2(-2 + x) + x(-2 + x)) + 2x
-2 + 4x2 = 4((-2 * 2 + x * 2) + x(-2 + x)) + 2x
-2 + 4x2 = 4((-4 + 2x) + x(-2 + x)) + 2x
-2 + 4x2 = 4(-4 + 2x + (-2 * x + x * x)) + 2x
-2 + 4x2 = 4(-4 + 2x + (-2x + x2)) + 2x

Combine like terms: 2x + -2x = 0
-2 + 4x2 = 4(-4 + 0 + x2) + 2x
-2 + 4x2 = 4(-4 + x2) + 2x
-2 + 4x2 = (-4 * 4 + x2 * 4) + 2x
-2 + 4x2 = (-16 + 4x2) + 2x

Reorder the terms:
-2 + 4x2 = -16 + 2x + 4x2

Add '-4x2' to each side of the equation.
-2 + 4x2 + -4x2 = -16 + 2x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-2 + 0 = -16 + 2x + 4x2 + -4x2
-2 = -16 + 2x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-2 = -16 + 2x + 0
-2 = -16 + 2x

Solving
-2 = -16 + 2x

Solving for variable 'x'.

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

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

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

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

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

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

Divide each side by '-2'.
x = 7

Simplifying
x = 7

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