3(x+15)-6x=-6x(x-3)

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Solution for 3(x+15)-6x=-6x(x-3) equation:


Simplifying
3(x + 15) + -6x = -6x(x + -3)

Reorder the terms:
3(15 + x) + -6x = -6x(x + -3)
(15 * 3 + x * 3) + -6x = -6x(x + -3)
(45 + 3x) + -6x = -6x(x + -3)

Combine like terms: 3x + -6x = -3x
45 + -3x = -6x(x + -3)

Reorder the terms:
45 + -3x = -6x(-3 + x)
45 + -3x = (-3 * -6x + x * -6x)
45 + -3x = (18x + -6x2)

Solving
45 + -3x = 18x + -6x2

Solving for variable 'x'.

Combine like terms: -3x + -18x = -21x
45 + -21x + 6x2 = 18x + -6x2 + -18x + 6x2

Reorder the terms:
45 + -21x + 6x2 = 18x + -18x + -6x2 + 6x2

Combine like terms: 18x + -18x = 0
45 + -21x + 6x2 = 0 + -6x2 + 6x2
45 + -21x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
45 + -21x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + -7x + 2x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(15 + -7x + 2x2)' equal to zero and attempt to solve: Simplifying 15 + -7x + 2x2 = 0 Solving 15 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -3.5x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -3.5x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -3.5x + x2 = 0 + -7.5 -3.5x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -3.5x + x2 = -7.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -7.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -7.5 + 3.0625 Combine like terms: -7.5 + 3.0625 = -4.4375 3.0625 + -3.5x + x2 = -4.4375 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = -4.4375 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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