(2x+7)(2x-7)=2+4(x-5)(x-5)

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Solution for (2x+7)(2x-7)=2+4(x-5)(x-5) equation: 


Simplifying
(2x + 7)(2x + -7) = 2 + 4(x + -5)(x + -5)

Reorder the terms:
(7 + 2x)(2x + -7) = 2 + 4(x + -5)(x + -5)

Reorder the terms:
(7 + 2x)(-7 + 2x) = 2 + 4(x + -5)(x + -5)

Multiply (7 + 2x) * (-7 + 2x)
(7(-7 + 2x) + 2x * (-7 + 2x)) = 2 + 4(x + -5)(x + -5)
((-7 * 7 + 2x * 7) + 2x * (-7 + 2x)) = 2 + 4(x + -5)(x + -5)
((-49 + 14x) + 2x * (-7 + 2x)) = 2 + 4(x + -5)(x + -5)
(-49 + 14x + (-7 * 2x + 2x * 2x)) = 2 + 4(x + -5)(x + -5)
(-49 + 14x + (-14x + 4x2)) = 2 + 4(x + -5)(x + -5)

Combine like terms: 14x + -14x = 0
(-49 + 0 + 4x2) = 2 + 4(x + -5)(x + -5)
(-49 + 4x2) = 2 + 4(x + -5)(x + -5)

Reorder the terms:
-49 + 4x2 = 2 + 4(-5 + x)(x + -5)

Reorder the terms:
-49 + 4x2 = 2 + 4(-5 + x)(-5 + x)

Multiply (-5 + x) * (-5 + x)
-49 + 4x2 = 2 + 4(-5(-5 + x) + x(-5 + x))
-49 + 4x2 = 2 + 4((-5 * -5 + x * -5) + x(-5 + x))
-49 + 4x2 = 2 + 4((25 + -5x) + x(-5 + x))
-49 + 4x2 = 2 + 4(25 + -5x + (-5 * x + x * x))
-49 + 4x2 = 2 + 4(25 + -5x + (-5x + x2))

Combine like terms: -5x + -5x = -10x
-49 + 4x2 = 2 + 4(25 + -10x + x2)
-49 + 4x2 = 2 + (25 * 4 + -10x * 4 + x2 * 4)
-49 + 4x2 = 2 + (100 + -40x + 4x2)

Combine like terms: 2 + 100 = 102
-49 + 4x2 = 102 + -40x + 4x2

Add '-4x2' to each side of the equation.
-49 + 4x2 + -4x2 = 102 + -40x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-49 + 0 = 102 + -40x + 4x2 + -4x2
-49 = 102 + -40x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-49 = 102 + -40x + 0
-49 = 102 + -40x

Solving
-49 = 102 + -40x

Solving for variable 'x'.

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

Add '40x' to each side of the equation.
-49 + 40x = 102 + -40x + 40x

Combine like terms: -40x + 40x = 0
-49 + 40x = 102 + 0
-49 + 40x = 102

Add '49' to each side of the equation.
-49 + 49 + 40x = 102 + 49

Combine like terms: -49 + 49 = 0
0 + 40x = 102 + 49
40x = 102 + 49

Combine like terms: 102 + 49 = 151
40x = 151

Divide each side by '40'.
x = 3.775

Simplifying
x = 3.775

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