10x^2-(x+2)(x+2)=x^2

Solution for 10x^2-(x+2)(x+2)=x^2 equation:

Simplifying
10x2 + -1(x + 2)(x + 2) = x2

Reorder the terms:
10x2 + -1(2 + x)(x + 2) = x2

Reorder the terms:
10x2 + -1(2 + x)(2 + x) = x2

Multiply (2 + x) * (2 + x)
10x2 + -1(2(2 + x) + x(2 + x)) = x2
10x2 + -1((2 * 2 + x * 2) + x(2 + x)) = x2
10x2 + -1((4 + 2x) + x(2 + x)) = x2
10x2 + -1(4 + 2x + (2 * x + x * x)) = x2
10x2 + -1(4 + 2x + (2x + x2)) = x2

Combine like terms: 2x + 2x = 4x
10x2 + -1(4 + 4x + x2) = x2
10x2 + (4 * -1 + 4x * -1 + x2 * -1) = x2
10x2 + (-4 + -4x + -1x2) = x2

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

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

Solving
-4 + -4x + 9x2 = x2

Solving for variable 'x'.

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

Combine like terms: x2 + -1x2 = 0
-4 + -4x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -1x + 2x2) = 0

Factor a trinomial.
4((-1 + -2x)(1 + -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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-0.5, 1}