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

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

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

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

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

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

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

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

Combine like terms: x2 + x2 = 2x2
4 + 4x + 2x2 = 10x2

Solving
4 + 4x + 2x2 = 10x2

Solving for variable 'x'.

Combine like terms: 2x2 + -10x2 = -8x2
4 + 4x + -8x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
4 + 4x + -8x2 = 0

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

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

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
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
Solution
x = {1, -0.5}