(3x+2)(-x)=4

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Solution for (3x+2)(-x)=4 equation:


Simplifying
(3x + 2)(-1x) = 4

Reorder the terms:
(2 + 3x)(-1x) = 4

Remove parenthesis around (-1x)
(2 + 3x) * -1x = 4

Reorder the terms for easier multiplication:
-1x(2 + 3x) = 4
(2 * -1x + 3x * -1x) = 4
(-2x + -3x2) = 4

Solving
-2x + -3x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + -2x + -3x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -2x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 2x + 3x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(4 + 2x + 3x2)' equal to zero and attempt to solve: Simplifying 4 + 2x + 3x2 = 0 Solving 4 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 0.6666666667x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 0.6666666667x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 0.6666666667x + x2 = 0 + -1.333333333 0.6666666667x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 0.6666666667x + x2 = -1.333333333 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = -1.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -1.333333333 + 0.1111111112 Combine like terms: -1.333333333 + 0.1111111112 = -1.2222222218 0.1111111112 + 0.6666666667x + x2 = -1.2222222218 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -1.2222222218 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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