5x+111=(2x+21)(2x+21)

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Solution for 5x+111=(2x+21)(2x+21) equation: 


Simplifying
5x + 111 = (2x + 21)(2x + 21)

Reorder the terms:
111 + 5x = (2x + 21)(2x + 21)

Reorder the terms:
111 + 5x = (21 + 2x)(2x + 21)

Reorder the terms:
111 + 5x = (21 + 2x)(21 + 2x)

Multiply (21 + 2x) * (21 + 2x)
111 + 5x = (21(21 + 2x) + 2x * (21 + 2x))
111 + 5x = ((21 * 21 + 2x * 21) + 2x * (21 + 2x))
111 + 5x = ((441 + 42x) + 2x * (21 + 2x))
111 + 5x = (441 + 42x + (21 * 2x + 2x * 2x))
111 + 5x = (441 + 42x + (42x + 4x2))

Combine like terms: 42x + 42x = 84x
111 + 5x = (441 + 84x + 4x2)

Solving
111 + 5x = 441 + 84x + 4x2

Solving for variable 'x'.

Reorder the terms:
111 + -441 + 5x + -84x + -4x2 = 441 + 84x + 4x2 + -441 + -84x + -4x2

Combine like terms: 111 + -441 = -330
-330 + 5x + -84x + -4x2 = 441 + 84x + 4x2 + -441 + -84x + -4x2

Combine like terms: 5x + -84x = -79x
-330 + -79x + -4x2 = 441 + 84x + 4x2 + -441 + -84x + -4x2

Reorder the terms:
-330 + -79x + -4x2 = 441 + -441 + 84x + -84x + 4x2 + -4x2

Combine like terms: 441 + -441 = 0
-330 + -79x + -4x2 = 0 + 84x + -84x + 4x2 + -4x2
-330 + -79x + -4x2 = 84x + -84x + 4x2 + -4x2

Combine like terms: 84x + -84x = 0
-330 + -79x + -4x2 = 0 + 4x2 + -4x2
-330 + -79x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-330 + -79x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(330 + 79x + 4x2) = 0

Factor a trinomial.
-1((55 + 4x)(6 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(55 + 4x)' equal to zero and attempt to solve:

Simplifying
55 + 4x = 0

Solving
55 + 4x = 0

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

Add '-55' to each side of the equation.
55 + -55 + 4x = 0 + -55

Combine like terms: 55 + -55 = 0
0 + 4x = 0 + -55
4x = 0 + -55

Combine like terms: 0 + -55 = -55
4x = -55

Divide each side by '4'.
x = -13.75

Simplifying
x = -13.75

Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {-13.75, -6}

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