x^2+(x+4)(x+4)=20(20)

Solution for x^2+(x+4)(x+4)=20(20) equation:

Simplifying
x2 + (x + 4)(x + 4) = 20(20)

Reorder the terms:
x2 + (4 + x)(x + 4) = 20(20)

Reorder the terms:
x2 + (4 + x)(4 + x) = 20(20)

Multiply (4 + x) * (4 + x)
x2 + (4(4 + x) + x(4 + x)) = 20(20)
x2 + ((4 * 4 + x * 4) + x(4 + x)) = 20(20)
x2 + ((16 + 4x) + x(4 + x)) = 20(20)
x2 + (16 + 4x + (4 * x + x * x)) = 20(20)
x2 + (16 + 4x + (4x + x2)) = 20(20)

Combine like terms: 4x + 4x = 8x
x2 + (16 + 8x + x2) = 20(20)

Reorder the terms:
16 + 8x + x2 + x2 = 20(20)

Combine like terms: x2 + x2 = 2x2
16 + 8x + 2x2 = 20(20)

Multiply 20 * 20
16 + 8x + 2x2 = 400

Solving
16 + 8x + 2x2 = 400

Solving for variable 'x'.

Reorder the terms:
16 + -400 + 8x + 2x2 = 400 + -400

Combine like terms: 16 + -400 = -384
-384 + 8x + 2x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-384 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-192 + 4x + x2) = 0

Factor a trinomial.
2((-16 + -1x)(12 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve:

Simplifying
-16 + -1x = 0

Solving
-16 + -1x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x = 0 + 16
-1x = 0 + 16

Combine like terms: 0 + 16 = 16
-1x = 16

Divide each side by '-1'.
x = -16

Simplifying
x = -16
Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-16, 12}