(9+2x)(19+2x)-171=288

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Solution for (9+2x)(19+2x)-171=288 equation: 


Simplifying
(9 + 2x)(19 + 2x) + -171 = 288

Multiply (9 + 2x) * (19 + 2x)
(9(19 + 2x) + 2x * (19 + 2x)) + -171 = 288
((19 * 9 + 2x * 9) + 2x * (19 + 2x)) + -171 = 288
((171 + 18x) + 2x * (19 + 2x)) + -171 = 288
(171 + 18x + (19 * 2x + 2x * 2x)) + -171 = 288
(171 + 18x + (38x + 4x2)) + -171 = 288

Combine like terms: 18x + 38x = 56x
(171 + 56x + 4x2) + -171 = 288

Reorder the terms:
171 + -171 + 56x + 4x2 = 288

Combine like terms: 171 + -171 = 0
0 + 56x + 4x2 = 288
56x + 4x2 = 288

Solving
56x + 4x2 = 288

Solving for variable 'x'.

Reorder the terms:
-288 + 56x + 4x2 = 288 + -288

Combine like terms: 288 + -288 = 0
-288 + 56x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-72 + 14x + x2) = 0

Factor a trinomial.
4((-18 + -1x)(4 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-18 + -1x)' equal to zero and attempt to solve:

Simplifying
-18 + -1x = 0

Solving
-18 + -1x = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1x = 0 + 18
-1x = 0 + 18

Combine like terms: 0 + 18 = 18
-1x = 18

Divide each side by '-1'.
x = -18

Simplifying
x = -18

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-18, 4}

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