9(x-1)(x-1)-(x+1)(x+1)=0

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Solution for 9(x-1)(x-1)-(x+1)(x+1)=0 equation:


Simplifying
9(x + -1)(x + -1) + -1(x + 1)(x + 1) = 0

Reorder the terms:
9(-1 + x)(x + -1) + -1(x + 1)(x + 1) = 0

Reorder the terms:
9(-1 + x)(-1 + x) + -1(x + 1)(x + 1) = 0

Multiply (-1 + x) * (-1 + x)
9(-1(-1 + x) + x(-1 + x)) + -1(x + 1)(x + 1) = 0
9((-1 * -1 + x * -1) + x(-1 + x)) + -1(x + 1)(x + 1) = 0
9((1 + -1x) + x(-1 + x)) + -1(x + 1)(x + 1) = 0
9(1 + -1x + (-1 * x + x * x)) + -1(x + 1)(x + 1) = 0
9(1 + -1x + (-1x + x2)) + -1(x + 1)(x + 1) = 0

Combine like terms: -1x + -1x = -2x
9(1 + -2x + x2) + -1(x + 1)(x + 1) = 0
(1 * 9 + -2x * 9 + x2 * 9) + -1(x + 1)(x + 1) = 0
(9 + -18x + 9x2) + -1(x + 1)(x + 1) = 0

Reorder the terms:
9 + -18x + 9x2 + -1(1 + x)(x + 1) = 0

Reorder the terms:
9 + -18x + 9x2 + -1(1 + x)(1 + x) = 0

Multiply (1 + x) * (1 + x)
9 + -18x + 9x2 + -1(1(1 + x) + x(1 + x)) = 0
9 + -18x + 9x2 + -1((1 * 1 + x * 1) + x(1 + x)) = 0
9 + -18x + 9x2 + -1((1 + 1x) + x(1 + x)) = 0
9 + -18x + 9x2 + -1(1 + 1x + (1 * x + x * x)) = 0
9 + -18x + 9x2 + -1(1 + 1x + (1x + x2)) = 0

Combine like terms: 1x + 1x = 2x
9 + -18x + 9x2 + -1(1 + 2x + x2) = 0
9 + -18x + 9x2 + (1 * -1 + 2x * -1 + x2 * -1) = 0
9 + -18x + 9x2 + (-1 + -2x + -1x2) = 0

Reorder the terms:
9 + -1 + -18x + -2x + 9x2 + -1x2 = 0

Combine like terms: 9 + -1 = 8
8 + -18x + -2x + 9x2 + -1x2 = 0

Combine like terms: -18x + -2x = -20x
8 + -20x + 9x2 + -1x2 = 0

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

Solving
8 + -20x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + -5x + 2x2) = 0

Factor a trinomial.
4((1 + -2x)(2 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.5, 2}

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