5x(3x+3)=3

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Solution for 5x(3x+3)=3 equation:


Simplifying
5x(3x + 3) = 3

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

Solving
15x + 15x2 = 3

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 5x + 5x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-1 + 5x + 5x2)' equal to zero and attempt to solve: Simplifying -1 + 5x + 5x2 = 0 Solving -1 + 5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x + x2 = 0 + 0.2 x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 x + x2 = 0.2 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.2 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.2 + 0.25 Combine like terms: 0.2 + 0.25 = 0.45 1.25 + x2 = 0.45 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.45 Calculate the square root of the right side: 0.670820393 Break this problem into two subproblems by setting (x + 0.5) equal to 0.670820393 and -0.670820393.

Subproblem 1

x + 0.5 = 0.670820393 Simplifying x + 0.5 = 0.670820393 Reorder the terms: 0.5 + x = 0.670820393 Solving 0.5 + x = 0.670820393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.670820393 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.670820393 + -0.5 x = 0.670820393 + -0.5 Combine like terms: 0.670820393 + -0.5 = 0.170820393 x = 0.170820393 Simplifying x = 0.170820393

Subproblem 2

x + 0.5 = -0.670820393 Simplifying x + 0.5 = -0.670820393 Reorder the terms: 0.5 + x = -0.670820393 Solving 0.5 + x = -0.670820393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.670820393 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.670820393 + -0.5 x = -0.670820393 + -0.5 Combine like terms: -0.670820393 + -0.5 = -1.170820393 x = -1.170820393 Simplifying x = -1.170820393

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.170820393, -1.170820393}

Solution

x = {0.170820393, -1.170820393}

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