288=(10+2x)(8+2x)

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Solution for 288=(10+2x)(8+2x) equation: 


Simplifying
288 = (10 + 2x)(8 + 2x)

Multiply (10 + 2x) * (8 + 2x)
288 = (10(8 + 2x) + 2x * (8 + 2x))
288 = ((8 * 10 + 2x * 10) + 2x * (8 + 2x))
288 = ((80 + 20x) + 2x * (8 + 2x))
288 = (80 + 20x + (8 * 2x + 2x * 2x))
288 = (80 + 20x + (16x + 4x2))

Combine like terms: 20x + 16x = 36x
288 = (80 + 36x + 4x2)

Solving
288 = 80 + 36x + 4x2

Solving for variable 'x'.

Combine like terms: 288 + -80 = 208
208 + -36x + -4x2 = 80 + 36x + 4x2 + -80 + -36x + -4x2

Reorder the terms:
208 + -36x + -4x2 = 80 + -80 + 36x + -36x + 4x2 + -4x2

Combine like terms: 80 + -80 = 0
208 + -36x + -4x2 = 0 + 36x + -36x + 4x2 + -4x2
208 + -36x + -4x2 = 36x + -36x + 4x2 + -4x2

Combine like terms: 36x + -36x = 0
208 + -36x + -4x2 = 0 + 4x2 + -4x2
208 + -36x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
208 + -36x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(52 + -9x + -1x2) = 0

Factor a trinomial.
4((4 + -1x)(13 + x)) = 0

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(13 + x)' equal to zero and attempt to solve:

Simplifying
13 + x = 0

Solving
13 + x = 0

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

Add '-13' to each side of the equation.
13 + -13 + x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + x = 0 + -13
x = 0 + -13

Combine like terms: 0 + -13 = -13
x = -13

Simplifying
x = -13
Solution
x = {4, -13}

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