(2x+7)(2x+7)=9

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Solution for (2x+7)(2x+7)=9 equation: 


Simplifying
(2x + 7)(2x + 7) = 9

Reorder the terms:
(7 + 2x)(2x + 7) = 9

Reorder the terms:
(7 + 2x)(7 + 2x) = 9

Multiply (7 + 2x) * (7 + 2x)
(7(7 + 2x) + 2x * (7 + 2x)) = 9
((7 * 7 + 2x * 7) + 2x * (7 + 2x)) = 9
((49 + 14x) + 2x * (7 + 2x)) = 9
(49 + 14x + (7 * 2x + 2x * 2x)) = 9
(49 + 14x + (14x + 4x2)) = 9

Combine like terms: 14x + 14x = 28x
(49 + 28x + 4x2) = 9

Solving
49 + 28x + 4x2 = 9

Solving for variable 'x'.

Reorder the terms:
49 + -9 + 28x + 4x2 = 9 + -9

Combine like terms: 49 + -9 = 40
40 + 28x + 4x2 = 9 + -9

Combine like terms: 9 + -9 = 0
40 + 28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(10 + 7x + x2) = 0

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

Ignore the factor 4.

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

Simplifying
5 + x = 0

Solving
5 + x = 0

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

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

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

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

Simplifying
x = -5

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-5, -2}

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