5x+105=(3x+13)(3x+13)

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Solution for 5x+105=(3x+13)(3x+13) equation: 


Simplifying
5x + 105 = (3x + 13)(3x + 13)

Reorder the terms:
105 + 5x = (3x + 13)(3x + 13)

Reorder the terms:
105 + 5x = (13 + 3x)(3x + 13)

Reorder the terms:
105 + 5x = (13 + 3x)(13 + 3x)

Multiply (13 + 3x) * (13 + 3x)
105 + 5x = (13(13 + 3x) + 3x * (13 + 3x))
105 + 5x = ((13 * 13 + 3x * 13) + 3x * (13 + 3x))
105 + 5x = ((169 + 39x) + 3x * (13 + 3x))
105 + 5x = (169 + 39x + (13 * 3x + 3x * 3x))
105 + 5x = (169 + 39x + (39x + 9x2))

Combine like terms: 39x + 39x = 78x
105 + 5x = (169 + 78x + 9x2)

Solving
105 + 5x = 169 + 78x + 9x2

Solving for variable 'x'.

Reorder the terms:
105 + -169 + 5x + -78x + -9x2 = 169 + 78x + 9x2 + -169 + -78x + -9x2

Combine like terms: 105 + -169 = -64
-64 + 5x + -78x + -9x2 = 169 + 78x + 9x2 + -169 + -78x + -9x2

Combine like terms: 5x + -78x = -73x
-64 + -73x + -9x2 = 169 + 78x + 9x2 + -169 + -78x + -9x2

Reorder the terms:
-64 + -73x + -9x2 = 169 + -169 + 78x + -78x + 9x2 + -9x2

Combine like terms: 169 + -169 = 0
-64 + -73x + -9x2 = 0 + 78x + -78x + 9x2 + -9x2
-64 + -73x + -9x2 = 78x + -78x + 9x2 + -9x2

Combine like terms: 78x + -78x = 0
-64 + -73x + -9x2 = 0 + 9x2 + -9x2
-64 + -73x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-64 + -73x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(64 + 73x + 9x2) = 0

Factor a trinomial.
-1((64 + 9x)(1 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(64 + 9x)' equal to zero and attempt to solve:

Simplifying
64 + 9x = 0

Solving
64 + 9x = 0

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

Add '-64' to each side of the equation.
64 + -64 + 9x = 0 + -64

Combine like terms: 64 + -64 = 0
0 + 9x = 0 + -64
9x = 0 + -64

Combine like terms: 0 + -64 = -64
9x = -64

Divide each side by '9'.
x = -7.111111111

Simplifying
x = -7.111111111

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 = {-7.111111111, -1}

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