0=-3x^3+24x^2+45x

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Solution for 0=-3x^3+24x^2+45x equation:


Simplifying
0 = -3x3 + 24x2 + 45x

Reorder the terms:
0 = 45x + 24x2 + -3x3

Solving
0 = 45x + 24x2 + -3x3

Solving for variable 'x'.
Remove the zero:
-45x + -24x2 + 3x3 = 45x + 24x2 + -3x3 + -45x + -24x2 + 3x3

Reorder the terms:
-45x + -24x2 + 3x3 = 45x + -45x + 24x2 + -24x2 + -3x3 + 3x3

Combine like terms: 45x + -45x = 0
-45x + -24x2 + 3x3 = 0 + 24x2 + -24x2 + -3x3 + 3x3
-45x + -24x2 + 3x3 = 24x2 + -24x2 + -3x3 + 3x3

Combine like terms: 24x2 + -24x2 = 0
-45x + -24x2 + 3x3 = 0 + -3x3 + 3x3
-45x + -24x2 + 3x3 = -3x3 + 3x3

Combine like terms: -3x3 + 3x3 = 0
-45x + -24x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-15 + -8x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(-15 + -8x + x2)' equal to zero and attempt to solve: Simplifying -15 + -8x + x2 = 0 Solving -15 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -8x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -8x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -8x + x2 = 0 + 15 -8x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -8x + x2 = 15 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 15 + 16 Reorder the terms: 16 + -8x + x2 = 15 + 16 Combine like terms: 15 + 16 = 31 16 + -8x + x2 = 31 Factor a perfect square on the left side: (x + -4)(x + -4) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + -4) equal to 5.567764363 and -5.567764363.

Subproblem 1

x + -4 = 5.567764363 Simplifying x + -4 = 5.567764363 Reorder the terms: -4 + x = 5.567764363 Solving -4 + x = 5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.567764363 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.567764363 + 4 x = 5.567764363 + 4 Combine like terms: 5.567764363 + 4 = 9.567764363 x = 9.567764363 Simplifying x = 9.567764363

Subproblem 2

x + -4 = -5.567764363 Simplifying x + -4 = -5.567764363 Reorder the terms: -4 + x = -5.567764363 Solving -4 + x = -5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.567764363 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.567764363 + 4 x = -5.567764363 + 4 Combine like terms: -5.567764363 + 4 = -1.567764363 x = -1.567764363 Simplifying x = -1.567764363

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.567764363, -1.567764363}

Solution

x = {0, 9.567764363, -1.567764363}

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