2(x+3)(x+3)+1=51

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Solution for 2(x+3)(x+3)+1=51 equation: 


Simplifying
2(x + 3)(x + 3) + 1 = 51

Reorder the terms:
2(3 + x)(x + 3) + 1 = 51

Reorder the terms:
2(3 + x)(3 + x) + 1 = 51

Multiply (3 + x) * (3 + x)
2(3(3 + x) + x(3 + x)) + 1 = 51
2((3 * 3 + x * 3) + x(3 + x)) + 1 = 51
2((9 + 3x) + x(3 + x)) + 1 = 51
2(9 + 3x + (3 * x + x * x)) + 1 = 51
2(9 + 3x + (3x + x2)) + 1 = 51

Combine like terms: 3x + 3x = 6x
2(9 + 6x + x2) + 1 = 51
(9 * 2 + 6x * 2 + x2 * 2) + 1 = 51
(18 + 12x + 2x2) + 1 = 51

Reorder the terms:
18 + 1 + 12x + 2x2 = 51

Combine like terms: 18 + 1 = 19
19 + 12x + 2x2 = 51

Solving
19 + 12x + 2x2 = 51

Solving for variable 'x'.

Reorder the terms:
19 + -51 + 12x + 2x2 = 51 + -51

Combine like terms: 19 + -51 = -32
-32 + 12x + 2x2 = 51 + -51

Combine like terms: 51 + -51 = 0
-32 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 6x + x2) = 0

Factor a trinomial.
2((-8 + -1x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

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

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

Divide each side by '-1'.
x = -8

Simplifying
x = -8

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 = {-8, 2}

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