(x+3)(x-7)+(x+5)(x-5)+4x=0

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Solution for (x+3)(x-7)+(x+5)(x-5)+4x=0 equation: 


Simplifying
(x + 3)(x + -7) + (x + 5)(x + -5) + 4x = 0

Reorder the terms:
(3 + x)(x + -7) + (x + 5)(x + -5) + 4x = 0

Reorder the terms:
(3 + x)(-7 + x) + (x + 5)(x + -5) + 4x = 0

Multiply (3 + x) * (-7 + x)
(3(-7 + x) + x(-7 + x)) + (x + 5)(x + -5) + 4x = 0
((-7 * 3 + x * 3) + x(-7 + x)) + (x + 5)(x + -5) + 4x = 0
((-21 + 3x) + x(-7 + x)) + (x + 5)(x + -5) + 4x = 0
(-21 + 3x + (-7 * x + x * x)) + (x + 5)(x + -5) + 4x = 0
(-21 + 3x + (-7x + x2)) + (x + 5)(x + -5) + 4x = 0

Combine like terms: 3x + -7x = -4x
(-21 + -4x + x2) + (x + 5)(x + -5) + 4x = 0

Reorder the terms:
-21 + -4x + x2 + (5 + x)(x + -5) + 4x = 0

Reorder the terms:
-21 + -4x + x2 + (5 + x)(-5 + x) + 4x = 0

Multiply (5 + x) * (-5 + x)
-21 + -4x + x2 + (5(-5 + x) + x(-5 + x)) + 4x = 0
-21 + -4x + x2 + ((-5 * 5 + x * 5) + x(-5 + x)) + 4x = 0
-21 + -4x + x2 + ((-25 + 5x) + x(-5 + x)) + 4x = 0
-21 + -4x + x2 + (-25 + 5x + (-5 * x + x * x)) + 4x = 0
-21 + -4x + x2 + (-25 + 5x + (-5x + x2)) + 4x = 0

Combine like terms: 5x + -5x = 0
-21 + -4x + x2 + (-25 + 0 + x2) + 4x = 0
-21 + -4x + x2 + (-25 + x2) + 4x = 0

Reorder the terms:
-21 + -25 + -4x + 4x + x2 + x2 = 0

Combine like terms: -21 + -25 = -46
-46 + -4x + 4x + x2 + x2 = 0

Combine like terms: -4x + 4x = 0
-46 + 0 + x2 + x2 = 0
-46 + x2 + x2 = 0

Combine like terms: x2 + x2 = 2x2
-46 + 2x2 = 0

Solving
-46 + 2x2 = 0

Solving for variable 'x'.

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

Add '46' to each side of the equation.
-46 + 46 + 2x2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + 2x2 = 0 + 46
2x2 = 0 + 46

Combine like terms: 0 + 46 = 46
2x2 = 46

Divide each side by '2'.
x2 = 23

Simplifying
x2 = 23

Take the square root of each side:
x = {-4.795831523, 4.795831523}

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