x^2+(3x+2)(3x+2)=212

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Solution for x^2+(3x+2)(3x+2)=212 equation: 


Simplifying
x2 + (3x + 2)(3x + 2) = 212

Reorder the terms:
x2 + (2 + 3x)(3x + 2) = 212

Reorder the terms:
x2 + (2 + 3x)(2 + 3x) = 212

Multiply (2 + 3x) * (2 + 3x)
x2 + (2(2 + 3x) + 3x * (2 + 3x)) = 212
x2 + ((2 * 2 + 3x * 2) + 3x * (2 + 3x)) = 212
x2 + ((4 + 6x) + 3x * (2 + 3x)) = 212
x2 + (4 + 6x + (2 * 3x + 3x * 3x)) = 212
x2 + (4 + 6x + (6x + 9x2)) = 212

Combine like terms: 6x + 6x = 12x
x2 + (4 + 12x + 9x2) = 212

Reorder the terms:
4 + 12x + x2 + 9x2 = 212

Combine like terms: x2 + 9x2 = 10x2
4 + 12x + 10x2 = 212

Solving
4 + 12x + 10x2 = 212

Solving for variable 'x'.

Reorder the terms:
4 + -212 + 12x + 10x2 = 212 + -212

Combine like terms: 4 + -212 = -208
-208 + 12x + 10x2 = 212 + -212

Combine like terms: 212 + -212 = 0
-208 + 12x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-104 + 6x + 5x2) = 0

Factor a trinomial.
2((-26 + -5x)(4 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-26 + -5x)' equal to zero and attempt to solve:

Simplifying
-26 + -5x = 0

Solving
-26 + -5x = 0

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

Add '26' to each side of the equation.
-26 + 26 + -5x = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -5x = 0 + 26
-5x = 0 + 26

Combine like terms: 0 + 26 = 26
-5x = 26

Divide each side by '-5'.
x = -5.2

Simplifying
x = -5.2

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-5.2, 4}

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