3(x+9)(x+3)=21x

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Solution for 3(x+9)(x+3)=21x equation:


Simplifying
3(x + 9)(x + 3) = 21x

Reorder the terms:
3(9 + x)(x + 3) = 21x

Reorder the terms:
3(9 + x)(3 + x) = 21x

Multiply (9 + x) * (3 + x)
3(9(3 + x) + x(3 + x)) = 21x
3((3 * 9 + x * 9) + x(3 + x)) = 21x
3((27 + 9x) + x(3 + x)) = 21x
3(27 + 9x + (3 * x + x * x)) = 21x
3(27 + 9x + (3x + x2)) = 21x

Combine like terms: 9x + 3x = 12x
3(27 + 12x + x2) = 21x
(27 * 3 + 12x * 3 + x2 * 3) = 21x
(81 + 36x + 3x2) = 21x

Solving
81 + 36x + 3x2 = 21x

Solving for variable 'x'.

Reorder the terms:
81 + 36x + -21x + 3x2 = 21x + -21x

Combine like terms: 36x + -21x = 15x
81 + 15x + 3x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
81 + 15x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(27 + 5x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(27 + 5x + x2)' equal to zero and attempt to solve: Simplifying 27 + 5x + x2 = 0 Solving 27 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + 5x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + 5x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 5x + x2 = 0 + -27 5x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 5x + x2 = -27 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -27 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -27 + 6.25 Combine like terms: -27 + 6.25 = -20.75 6.25 + 5x + x2 = -20.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -20.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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