3x(-4x+2)=13x+9

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Solution for 3x(-4x+2)=13x+9 equation:


Simplifying
3x(-4x + 2) = 13x + 9

Reorder the terms:
3x(2 + -4x) = 13x + 9
(2 * 3x + -4x * 3x) = 13x + 9
(6x + -12x2) = 13x + 9

Reorder the terms:
6x + -12x2 = 9 + 13x

Solving
6x + -12x2 = 9 + 13x

Solving for variable 'x'.

Reorder the terms:
-9 + 6x + -13x + -12x2 = 9 + 13x + -9 + -13x

Combine like terms: 6x + -13x = -7x
-9 + -7x + -12x2 = 9 + 13x + -9 + -13x

Reorder the terms:
-9 + -7x + -12x2 = 9 + -9 + 13x + -13x

Combine like terms: 9 + -9 = 0
-9 + -7x + -12x2 = 0 + 13x + -13x
-9 + -7x + -12x2 = 13x + -13x

Combine like terms: 13x + -13x = 0
-9 + -7x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 7x + 12x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(9 + 7x + 12x2)' equal to zero and attempt to solve: Simplifying 9 + 7x + 12x2 = 0 Solving 9 + 7x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.75 + 0.5833333333x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 0.5833333333x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 0.5833333333x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 0.5833333333x + x2 = 0 + -0.75 0.5833333333x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 0.5833333333x + x2 = -0.75 The x term is 0.5833333333x. Take half its coefficient (0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. 0.5833333333x + 0.08506944446 + x2 = -0.75 + 0.08506944446 Reorder the terms: 0.08506944446 + 0.5833333333x + x2 = -0.75 + 0.08506944446 Combine like terms: -0.75 + 0.08506944446 = -0.66493055554 0.08506944446 + 0.5833333333x + x2 = -0.66493055554 Factor a perfect square on the left side: (x + 0.2916666667)(x + 0.2916666667) = -0.66493055554 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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