6x-54=-3x(x+45)

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Solution for 6x-54=-3x(x+45) equation:


Simplifying
6x + -54 = -3x(x + 45)

Reorder the terms:
-54 + 6x = -3x(x + 45)

Reorder the terms:
-54 + 6x = -3x(45 + x)
-54 + 6x = (45 * -3x + x * -3x)
-54 + 6x = (-135x + -3x2)

Solving
-54 + 6x = -135x + -3x2

Solving for variable 'x'.

Combine like terms: 6x + 135x = 141x
-54 + 141x + 3x2 = -135x + -3x2 + 135x + 3x2

Reorder the terms:
-54 + 141x + 3x2 = -135x + 135x + -3x2 + 3x2

Combine like terms: -135x + 135x = 0
-54 + 141x + 3x2 = 0 + -3x2 + 3x2
-54 + 141x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-54 + 141x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + 47x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-18 + 47x + x2)' equal to zero and attempt to solve: Simplifying -18 + 47x + x2 = 0 Solving -18 + 47x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 47x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 47x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 47x + x2 = 0 + 18 47x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 47x + x2 = 18 The x term is 47x. Take half its coefficient (23.5). Square it (552.25) and add it to both sides. Add '552.25' to each side of the equation. 47x + 552.25 + x2 = 18 + 552.25 Reorder the terms: 552.25 + 47x + x2 = 18 + 552.25 Combine like terms: 18 + 552.25 = 570.25 552.25 + 47x + x2 = 570.25 Factor a perfect square on the left side: (x + 23.5)(x + 23.5) = 570.25 Calculate the square root of the right side: 23.879907873 Break this problem into two subproblems by setting (x + 23.5) equal to 23.879907873 and -23.879907873.

Subproblem 1

x + 23.5 = 23.879907873 Simplifying x + 23.5 = 23.879907873 Reorder the terms: 23.5 + x = 23.879907873 Solving 23.5 + x = 23.879907873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23.5' to each side of the equation. 23.5 + -23.5 + x = 23.879907873 + -23.5 Combine like terms: 23.5 + -23.5 = 0.0 0.0 + x = 23.879907873 + -23.5 x = 23.879907873 + -23.5 Combine like terms: 23.879907873 + -23.5 = 0.379907873 x = 0.379907873 Simplifying x = 0.379907873

Subproblem 2

x + 23.5 = -23.879907873 Simplifying x + 23.5 = -23.879907873 Reorder the terms: 23.5 + x = -23.879907873 Solving 23.5 + x = -23.879907873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23.5' to each side of the equation. 23.5 + -23.5 + x = -23.879907873 + -23.5 Combine like terms: 23.5 + -23.5 = 0.0 0.0 + x = -23.879907873 + -23.5 x = -23.879907873 + -23.5 Combine like terms: -23.879907873 + -23.5 = -47.379907873 x = -47.379907873 Simplifying x = -47.379907873

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.379907873, -47.379907873}

Solution

x = {0.379907873, -47.379907873}

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