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Simplifying 3x^{2}+ -6x + 12 = 0 Reorder the terms: 12 + -6x + 3x^{2}= 0 Solving 12 + -6x + 3x^{2}= 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -2x + x^{2}) = 0 Ignore the factor 3.## Subproblem 1

Set the factor '(4 + -2x + x^{2})' equal to zero and attempt to solve: Simplifying 4 + -2x + x^{2}= 0 Solving 4 + -2x + x^{2}= 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -2x + -4 + x^{2}= 0 + -4 Reorder the terms: 4 + -4 + -2x + x^{2}= 0 + -4 Combine like terms: 4 + -4 = 0 0 + -2x + x^{2}= 0 + -4 -2x + x^{2}= 0 + -4 Combine like terms: 0 + -4 = -4 -2x + x^{2}= -4 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 + x^{2}= -4 + 1 Reorder the terms: 1 + -2x + x^{2}= -4 + 1 Combine like terms: -4 + 1 = -3 1 + -2x + x^{2}= -3 Factor a perfect square on the left side: (x + -1)(x + -1) = -3 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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