-3(x+7)+69=3x-6x(x-1)

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Solution for -3(x+7)+69=3x-6x(x-1) equation:


Simplifying
-3(x + 7) + 69 = 3x + -6x(x + -1)

Reorder the terms:
-3(7 + x) + 69 = 3x + -6x(x + -1)
(7 * -3 + x * -3) + 69 = 3x + -6x(x + -1)
(-21 + -3x) + 69 = 3x + -6x(x + -1)

Reorder the terms:
-21 + 69 + -3x = 3x + -6x(x + -1)

Combine like terms: -21 + 69 = 48
48 + -3x = 3x + -6x(x + -1)

Reorder the terms:
48 + -3x = 3x + -6x(-1 + x)
48 + -3x = 3x + (-1 * -6x + x * -6x)
48 + -3x = 3x + (6x + -6x2)

Combine like terms: 3x + 6x = 9x
48 + -3x = 9x + -6x2

Solving
48 + -3x = 9x + -6x2

Solving for variable 'x'.

Combine like terms: -3x + -9x = -12x
48 + -12x + 6x2 = 9x + -6x2 + -9x + 6x2

Reorder the terms:
48 + -12x + 6x2 = 9x + -9x + -6x2 + 6x2

Combine like terms: 9x + -9x = 0
48 + -12x + 6x2 = 0 + -6x2 + 6x2
48 + -12x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
48 + -12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(8 + -2x + x2) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(8 + -2x + x2)' equal to zero and attempt to solve: Simplifying 8 + -2x + x2 = 0 Solving 8 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -2x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -2x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -2x + x2 = 0 + -8 -2x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -2x + x2 = -8 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -8 + 1 Reorder the terms: 1 + -2x + x2 = -8 + 1 Combine like terms: -8 + 1 = -7 1 + -2x + x2 = -7 Factor a perfect square on the left side: (x + -1)(x + -1) = -7 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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