(2x+15)(2x+15)=169

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Solution for (2x+15)(2x+15)=169 equation: 


Simplifying
(2x + 15)(2x + 15) = 169

Reorder the terms:
(15 + 2x)(2x + 15) = 169

Reorder the terms:
(15 + 2x)(15 + 2x) = 169

Multiply (15 + 2x) * (15 + 2x)
(15(15 + 2x) + 2x * (15 + 2x)) = 169
((15 * 15 + 2x * 15) + 2x * (15 + 2x)) = 169
((225 + 30x) + 2x * (15 + 2x)) = 169
(225 + 30x + (15 * 2x + 2x * 2x)) = 169
(225 + 30x + (30x + 4x2)) = 169

Combine like terms: 30x + 30x = 60x
(225 + 60x + 4x2) = 169

Solving
225 + 60x + 4x2 = 169

Solving for variable 'x'.

Reorder the terms:
225 + -169 + 60x + 4x2 = 169 + -169

Combine like terms: 225 + -169 = 56
56 + 60x + 4x2 = 169 + -169

Combine like terms: 169 + -169 = 0
56 + 60x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(14 + 15x + x2) = 0

Factor a trinomial.
4((14 + x)(1 + x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(14 + x)' equal to zero and attempt to solve:

Simplifying
14 + x = 0

Solving
14 + x = 0

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

Add '-14' to each side of the equation.
14 + -14 + x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + x = 0 + -14
x = 0 + -14

Combine like terms: 0 + -14 = -14
x = -14

Simplifying
x = -14

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-14, -1}

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