(3x+2)(2x+3)=15x

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Solution for (3x+2)(2x+3)=15x equation:


Simplifying
(3x + 2)(2x + 3) = 15x

Reorder the terms:
(2 + 3x)(2x + 3) = 15x

Reorder the terms:
(2 + 3x)(3 + 2x) = 15x

Multiply (2 + 3x) * (3 + 2x)
(2(3 + 2x) + 3x * (3 + 2x)) = 15x
((3 * 2 + 2x * 2) + 3x * (3 + 2x)) = 15x
((6 + 4x) + 3x * (3 + 2x)) = 15x
(6 + 4x + (3 * 3x + 2x * 3x)) = 15x
(6 + 4x + (9x + 6x2)) = 15x

Combine like terms: 4x + 9x = 13x
(6 + 13x + 6x2) = 15x

Solving
6 + 13x + 6x2 = 15x

Solving for variable 'x'.

Reorder the terms:
6 + 13x + -15x + 6x2 = 15x + -15x

Combine like terms: 13x + -15x = -2x
6 + -2x + 6x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
6 + -2x + 6x2 = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying 3 + -1x + 3x2 = 0 Solving 3 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.3333333333x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -0.3333333333x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.3333333333x + x2 = 0 + -1 -0.3333333333x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.3333333333x + x2 = -1 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = -1 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = -1 + 0.02777777779 Combine like terms: -1 + 0.02777777779 = -0.97222222221 0.02777777779 + -0.3333333333x + x2 = -0.97222222221 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = -0.97222222221 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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