3x(x-5)=6x-15

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Solution for 3x(x-5)=6x-15 equation:


Simplifying
3x(x + -5) = 6x + -15

Reorder the terms:
3x(-5 + x) = 6x + -15
(-5 * 3x + x * 3x) = 6x + -15
(-15x + 3x2) = 6x + -15

Reorder the terms:
-15x + 3x2 = -15 + 6x

Solving
-15x + 3x2 = -15 + 6x

Solving for variable 'x'.

Reorder the terms:
15 + -15x + -6x + 3x2 = -15 + 6x + 15 + -6x

Combine like terms: -15x + -6x = -21x
15 + -21x + 3x2 = -15 + 6x + 15 + -6x

Reorder the terms:
15 + -21x + 3x2 = -15 + 15 + 6x + -6x

Combine like terms: -15 + 15 = 0
15 + -21x + 3x2 = 0 + 6x + -6x
15 + -21x + 3x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
15 + -21x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -7x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(5 + -7x + x2)' equal to zero and attempt to solve: Simplifying 5 + -7x + x2 = 0 Solving 5 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -7x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -7x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7x + x2 = 0 + -5 -7x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -7x + x2 = -5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -5 + 12.25 Combine like terms: -5 + 12.25 = 7.25 12.25 + -7x + x2 = 7.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + -3.5) equal to 2.692582404 and -2.692582404.

Subproblem 1

x + -3.5 = 2.692582404 Simplifying x + -3.5 = 2.692582404 Reorder the terms: -3.5 + x = 2.692582404 Solving -3.5 + x = 2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 2.692582404 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.692582404 + 3.5 x = 2.692582404 + 3.5 Combine like terms: 2.692582404 + 3.5 = 6.192582404 x = 6.192582404 Simplifying x = 6.192582404

Subproblem 2

x + -3.5 = -2.692582404 Simplifying x + -3.5 = -2.692582404 Reorder the terms: -3.5 + x = -2.692582404 Solving -3.5 + x = -2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -2.692582404 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.692582404 + 3.5 x = -2.692582404 + 3.5 Combine like terms: -2.692582404 + 3.5 = 0.807417596 x = 0.807417596 Simplifying x = 0.807417596

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.192582404, 0.807417596}

Solution

x = {6.192582404, 0.807417596}

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