(x-4)(x-4)-(x+5)(x+5)-5(1-4x)=0

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Solution for (x-4)(x-4)-(x+5)(x+5)-5(1-4x)=0 equation: 


Simplifying
(x + -4)(x + -4) + -1(x + 5)(x + 5) + -5(1 + -4x) = 0

Reorder the terms:
(-4 + x)(x + -4) + -1(x + 5)(x + 5) + -5(1 + -4x) = 0

Reorder the terms:
(-4 + x)(-4 + x) + -1(x + 5)(x + 5) + -5(1 + -4x) = 0

Multiply (-4 + x) * (-4 + x)
(-4(-4 + x) + x(-4 + x)) + -1(x + 5)(x + 5) + -5(1 + -4x) = 0
((-4 * -4 + x * -4) + x(-4 + x)) + -1(x + 5)(x + 5) + -5(1 + -4x) = 0
((16 + -4x) + x(-4 + x)) + -1(x + 5)(x + 5) + -5(1 + -4x) = 0
(16 + -4x + (-4 * x + x * x)) + -1(x + 5)(x + 5) + -5(1 + -4x) = 0
(16 + -4x + (-4x + x2)) + -1(x + 5)(x + 5) + -5(1 + -4x) = 0

Combine like terms: -4x + -4x = -8x
(16 + -8x + x2) + -1(x + 5)(x + 5) + -5(1 + -4x) = 0

Reorder the terms:
16 + -8x + x2 + -1(5 + x)(x + 5) + -5(1 + -4x) = 0

Reorder the terms:
16 + -8x + x2 + -1(5 + x)(5 + x) + -5(1 + -4x) = 0

Multiply (5 + x) * (5 + x)
16 + -8x + x2 + -1(5(5 + x) + x(5 + x)) + -5(1 + -4x) = 0
16 + -8x + x2 + -1((5 * 5 + x * 5) + x(5 + x)) + -5(1 + -4x) = 0
16 + -8x + x2 + -1((25 + 5x) + x(5 + x)) + -5(1 + -4x) = 0
16 + -8x + x2 + -1(25 + 5x + (5 * x + x * x)) + -5(1 + -4x) = 0
16 + -8x + x2 + -1(25 + 5x + (5x + x2)) + -5(1 + -4x) = 0

Combine like terms: 5x + 5x = 10x
16 + -8x + x2 + -1(25 + 10x + x2) + -5(1 + -4x) = 0
16 + -8x + x2 + (25 * -1 + 10x * -1 + x2 * -1) + -5(1 + -4x) = 0
16 + -8x + x2 + (-25 + -10x + -1x2) + -5(1 + -4x) = 0
16 + -8x + x2 + -25 + -10x + -1x2 + (1 * -5 + -4x * -5) = 0
16 + -8x + x2 + -25 + -10x + -1x2 + (-5 + 20x) = 0

Reorder the terms:
16 + -25 + -5 + -8x + -10x + 20x + x2 + -1x2 = 0

Combine like terms: 16 + -25 = -9
-9 + -5 + -8x + -10x + 20x + x2 + -1x2 = 0

Combine like terms: -9 + -5 = -14
-14 + -8x + -10x + 20x + x2 + -1x2 = 0

Combine like terms: -8x + -10x = -18x
-14 + -18x + 20x + x2 + -1x2 = 0

Combine like terms: -18x + 20x = 2x
-14 + 2x + x2 + -1x2 = 0

Combine like terms: x2 + -1x2 = 0
-14 + 2x + 0 = 0
-14 + 2x = 0

Solving
-14 + 2x = 0

Solving for variable 'x'.

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

Add '14' to each side of the equation.
-14 + 14 + 2x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 2x = 0 + 14
2x = 0 + 14

Combine like terms: 0 + 14 = 14
2x = 14

Divide each side by '2'.
x = 7

Simplifying
x = 7

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