3x(9x+6)=(20x+4)18

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Solution for 3x(9x+6)=(20x+4)18 equation:


Simplifying
3x(9x + 6) = (20x + 4) * 18

Reorder the terms:
3x(6 + 9x) = (20x + 4) * 18
(6 * 3x + 9x * 3x) = (20x + 4) * 18
(18x + 27x2) = (20x + 4) * 18

Reorder the terms:
18x + 27x2 = (4 + 20x) * 18

Reorder the terms for easier multiplication:
18x + 27x2 = 18(4 + 20x)
18x + 27x2 = (4 * 18 + 20x * 18)
18x + 27x2 = (72 + 360x)

Solving
18x + 27x2 = 72 + 360x

Solving for variable 'x'.

Reorder the terms:
-72 + 18x + -360x + 27x2 = 72 + 360x + -72 + -360x

Combine like terms: 18x + -360x = -342x
-72 + -342x + 27x2 = 72 + 360x + -72 + -360x

Reorder the terms:
-72 + -342x + 27x2 = 72 + -72 + 360x + -360x

Combine like terms: 72 + -72 = 0
-72 + -342x + 27x2 = 0 + 360x + -360x
-72 + -342x + 27x2 = 360x + -360x

Combine like terms: 360x + -360x = 0
-72 + -342x + 27x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-8 + -38x + 3x2) = 0

Ignore the factor 9.

Subproblem 1

Set the factor '(-8 + -38x + 3x2)' equal to zero and attempt to solve: Simplifying -8 + -38x + 3x2 = 0 Solving -8 + -38x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + -12.66666667x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -12.66666667x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -12.66666667x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -12.66666667x + x2 = 0 + 2.666666667 -12.66666667x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -12.66666667x + x2 = 2.666666667 The x term is -12.66666667x. Take half its coefficient (-6.333333335). Square it (40.11111113) and add it to both sides. Add '40.11111113' to each side of the equation. -12.66666667x + 40.11111113 + x2 = 2.666666667 + 40.11111113 Reorder the terms: 40.11111113 + -12.66666667x + x2 = 2.666666667 + 40.11111113 Combine like terms: 2.666666667 + 40.11111113 = 42.777777797 40.11111113 + -12.66666667x + x2 = 42.777777797 Factor a perfect square on the left side: (x + -6.333333335)(x + -6.333333335) = 42.777777797 Calculate the square root of the right side: 6.540472292 Break this problem into two subproblems by setting (x + -6.333333335) equal to 6.540472292 and -6.540472292.

Subproblem 1

x + -6.333333335 = 6.540472292 Simplifying x + -6.333333335 = 6.540472292 Reorder the terms: -6.333333335 + x = 6.540472292 Solving -6.333333335 + x = 6.540472292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.333333335' to each side of the equation. -6.333333335 + 6.333333335 + x = 6.540472292 + 6.333333335 Combine like terms: -6.333333335 + 6.333333335 = 0.000000000 0.000000000 + x = 6.540472292 + 6.333333335 x = 6.540472292 + 6.333333335 Combine like terms: 6.540472292 + 6.333333335 = 12.873805627 x = 12.873805627 Simplifying x = 12.873805627

Subproblem 2

x + -6.333333335 = -6.540472292 Simplifying x + -6.333333335 = -6.540472292 Reorder the terms: -6.333333335 + x = -6.540472292 Solving -6.333333335 + x = -6.540472292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.333333335' to each side of the equation. -6.333333335 + 6.333333335 + x = -6.540472292 + 6.333333335 Combine like terms: -6.333333335 + 6.333333335 = 0.000000000 0.000000000 + x = -6.540472292 + 6.333333335 x = -6.540472292 + 6.333333335 Combine like terms: -6.540472292 + 6.333333335 = -0.207138957 x = -0.207138957 Simplifying x = -0.207138957

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.873805627, -0.207138957}

Solution

x = {12.873805627, -0.207138957}

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