3x(5x-240)=15

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Solution for 3x(5x-240)=15 equation:


Simplifying
3x(5x + -240) = 15

Reorder the terms:
3x(-240 + 5x) = 15
(-240 * 3x + 5x * 3x) = 15
(-720x + 15x2) = 15

Solving
-720x + 15x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + -720x + 15x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -720x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-1 + -48x + x2) = 0

Ignore the factor 15.

Subproblem 1

Set the factor '(-1 + -48x + x2)' equal to zero and attempt to solve: Simplifying -1 + -48x + x2 = 0 Solving -1 + -48x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -48x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -48x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -48x + x2 = 0 + 1 -48x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -48x + x2 = 1 The x term is -48x. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48x + 576 + x2 = 1 + 576 Reorder the terms: 576 + -48x + x2 = 1 + 576 Combine like terms: 1 + 576 = 577 576 + -48x + x2 = 577 Factor a perfect square on the left side: (x + -24)(x + -24) = 577 Calculate the square root of the right side: 24.020824299 Break this problem into two subproblems by setting (x + -24) equal to 24.020824299 and -24.020824299.

Subproblem 1

x + -24 = 24.020824299 Simplifying x + -24 = 24.020824299 Reorder the terms: -24 + x = 24.020824299 Solving -24 + x = 24.020824299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 24.020824299 + 24 Combine like terms: -24 + 24 = 0 0 + x = 24.020824299 + 24 x = 24.020824299 + 24 Combine like terms: 24.020824299 + 24 = 48.020824299 x = 48.020824299 Simplifying x = 48.020824299

Subproblem 2

x + -24 = -24.020824299 Simplifying x + -24 = -24.020824299 Reorder the terms: -24 + x = -24.020824299 Solving -24 + x = -24.020824299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = -24.020824299 + 24 Combine like terms: -24 + 24 = 0 0 + x = -24.020824299 + 24 x = -24.020824299 + 24 Combine like terms: -24.020824299 + 24 = -0.020824299 x = -0.020824299 Simplifying x = -0.020824299

Solution

The solution to the problem is based on the solutions from the subproblems. x = {48.020824299, -0.020824299}

Solution

x = {48.020824299, -0.020824299}

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