5x-6=4x(x-1)+x

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Solution for 5x-6=4x(x-1)+x equation:


Simplifying
5x + -6 = 4x(x + -1) + x

Reorder the terms:
-6 + 5x = 4x(x + -1) + x

Reorder the terms:
-6 + 5x = 4x(-1 + x) + x
-6 + 5x = (-1 * 4x + x * 4x) + x
-6 + 5x = (-4x + 4x2) + x

Reorder the terms:
-6 + 5x = -4x + x + 4x2

Combine like terms: -4x + x = -3x
-6 + 5x = -3x + 4x2

Solving
-6 + 5x = -3x + 4x2

Solving for variable 'x'.

Combine like terms: 5x + 3x = 8x
-6 + 8x + -4x2 = -3x + 4x2 + 3x + -4x2

Reorder the terms:
-6 + 8x + -4x2 = -3x + 3x + 4x2 + -4x2

Combine like terms: -3x + 3x = 0
-6 + 8x + -4x2 = 0 + 4x2 + -4x2
-6 + 8x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-6 + 8x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 4x + -2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-3 + 4x + -2x2)' equal to zero and attempt to solve: Simplifying -3 + 4x + -2x2 = 0 Solving -3 + 4x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1.5 + -2x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -2x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -2x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -2x + x2 = 0 + -1.5 -2x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -2x + x2 = -1.5 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 = -1.5 + 1 Reorder the terms: 1 + -2x + x2 = -1.5 + 1 Combine like terms: -1.5 + 1 = -0.5 1 + -2x + x2 = -0.5 Factor a perfect square on the left side: (x + -1)(x + -1) = -0.5 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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