11x-(4-x)*(1+x)=1+(x-3)*(x-3)

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Solution for 11x-(4-x)*(1+x)=1+(x-3)*(x-3) equation: 


Simplifying
11x + -1(4 + -1x)(1 + x) = 1 + (x + -3)(x + -3)

Multiply (4 + -1x) * (1 + x)
11x + -1(4(1 + x) + -1x * (1 + x)) = 1 + (x + -3)(x + -3)
11x + -1((1 * 4 + x * 4) + -1x * (1 + x)) = 1 + (x + -3)(x + -3)
11x + -1((4 + 4x) + -1x * (1 + x)) = 1 + (x + -3)(x + -3)
11x + -1(4 + 4x + (1 * -1x + x * -1x)) = 1 + (x + -3)(x + -3)
11x + -1(4 + 4x + (-1x + -1x2)) = 1 + (x + -3)(x + -3)

Combine like terms: 4x + -1x = 3x
11x + -1(4 + 3x + -1x2) = 1 + (x + -3)(x + -3)
11x + (4 * -1 + 3x * -1 + -1x2 * -1) = 1 + (x + -3)(x + -3)
11x + (-4 + -3x + 1x2) = 1 + (x + -3)(x + -3)

Reorder the terms:
-4 + 11x + -3x + 1x2 = 1 + (x + -3)(x + -3)

Combine like terms: 11x + -3x = 8x
-4 + 8x + 1x2 = 1 + (x + -3)(x + -3)

Reorder the terms:
-4 + 8x + 1x2 = 1 + (-3 + x)(x + -3)

Reorder the terms:
-4 + 8x + 1x2 = 1 + (-3 + x)(-3 + x)

Multiply (-3 + x) * (-3 + x)
-4 + 8x + 1x2 = 1 + (-3(-3 + x) + x(-3 + x))
-4 + 8x + 1x2 = 1 + ((-3 * -3 + x * -3) + x(-3 + x))
-4 + 8x + 1x2 = 1 + ((9 + -3x) + x(-3 + x))
-4 + 8x + 1x2 = 1 + (9 + -3x + (-3 * x + x * x))
-4 + 8x + 1x2 = 1 + (9 + -3x + (-3x + x2))

Combine like terms: -3x + -3x = -6x
-4 + 8x + 1x2 = 1 + (9 + -6x + x2)

Combine like terms: 1 + 9 = 10
-4 + 8x + 1x2 = 10 + -6x + x2

Solving
-4 + 8x + 1x2 = 10 + -6x + x2

Solving for variable 'x'.

Reorder the terms:
-4 + -10 + 8x + 6x + 1x2 + -1x2 = 10 + -6x + x2 + -10 + 6x + -1x2

Combine like terms: -4 + -10 = -14
-14 + 8x + 6x + 1x2 + -1x2 = 10 + -6x + x2 + -10 + 6x + -1x2

Combine like terms: 8x + 6x = 14x
-14 + 14x + 1x2 + -1x2 = 10 + -6x + x2 + -10 + 6x + -1x2

Combine like terms: 1x2 + -1x2 = 0
-14 + 14x + 0 = 10 + -6x + x2 + -10 + 6x + -1x2
-14 + 14x = 10 + -6x + x2 + -10 + 6x + -1x2

Reorder the terms:
-14 + 14x = 10 + -10 + -6x + 6x + x2 + -1x2

Combine like terms: 10 + -10 = 0
-14 + 14x = 0 + -6x + 6x + x2 + -1x2
-14 + 14x = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-14 + 14x = 0 + x2 + -1x2
-14 + 14x = x2 + -1x2

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

Factor out the Greatest Common Factor (GCF), '14'.
14(-1 + x) = 0

Ignore the factor 14.

Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

Add '1' to each side of the equation.
-1 + 1 + x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0 + 1
x = 0 + 1

Combine like terms: 0 + 1 = 1
x = 1

Simplifying
x = 1
Solution
x = {1}

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