3x+x(5x-7x)=12-x

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Solution for 3x+x(5x-7x)=12-x equation:


Simplifying
3x + x(5x + -7x) = 12 + -1x

Combine like terms: 5x + -7x = -2x
3x + x(-2x) = 12 + -1x

Remove parenthesis around (-2x)
3x + x * -2x = 12 + -1x

Reorder the terms for easier multiplication:
3x + -2x * x = 12 + -1x

Multiply x * x
3x + -2x2 = 12 + -1x

Solving
3x + -2x2 = 12 + -1x

Solving for variable 'x'.

Reorder the terms:
-12 + 3x + x + -2x2 = 12 + -1x + -12 + x

Combine like terms: 3x + x = 4x
-12 + 4x + -2x2 = 12 + -1x + -12 + x

Reorder the terms:
-12 + 4x + -2x2 = 12 + -12 + -1x + x

Combine like terms: 12 + -12 = 0
-12 + 4x + -2x2 = 0 + -1x + x
-12 + 4x + -2x2 = -1x + x

Combine like terms: -1x + x = 0
-12 + 4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 2x + -1x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-6 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying -6 + 2x + -1x2 = 0 Solving -6 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6 + -2x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -2x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -2x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -2x + x2 = 0 + -6 -2x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -2x + x2 = -6 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 = -6 + 1 Reorder the terms: 1 + -2x + x2 = -6 + 1 Combine like terms: -6 + 1 = -5 1 + -2x + x2 = -5 Factor a perfect square on the left side: (x + -1)(x + -1) = -5 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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