(3x+3)*x*85=180

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Solution for (3x+3)*x*85=180 equation:


Simplifying
(3x + 3) * x * 85 = 180

Reorder the terms:
(3 + 3x) * x * 85 = 180

Reorder the terms for easier multiplication:
85x(3 + 3x) = 180
(3 * 85x + 3x * 85x) = 180
(255x + 255x2) = 180

Solving
255x + 255x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 255x + 255x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 255x + 255x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-12 + 17x + 17x2) = 0

Ignore the factor 15.

Subproblem 1

Set the factor '(-12 + 17x + 17x2)' equal to zero and attempt to solve: Simplifying -12 + 17x + 17x2 = 0 Solving -12 + 17x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.7058823529 + x + x2 = 0 Move the constant term to the right: Add '0.7058823529' to each side of the equation. -0.7058823529 + x + 0.7058823529 + x2 = 0 + 0.7058823529 Reorder the terms: -0.7058823529 + 0.7058823529 + x + x2 = 0 + 0.7058823529 Combine like terms: -0.7058823529 + 0.7058823529 = 0.0000000000 0.0000000000 + x + x2 = 0 + 0.7058823529 x + x2 = 0 + 0.7058823529 Combine like terms: 0 + 0.7058823529 = 0.7058823529 x + x2 = 0.7058823529 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 = 0.7058823529 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.7058823529 + 0.25 Combine like terms: 0.7058823529 + 0.25 = 0.9558823529 1.25 + x2 = 0.9558823529 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.9558823529 Calculate the square root of the right side: 0.977692361 Break this problem into two subproblems by setting (x + 0.5) equal to 0.977692361 and -0.977692361.

Subproblem 1

x + 0.5 = 0.977692361 Simplifying x + 0.5 = 0.977692361 Reorder the terms: 0.5 + x = 0.977692361 Solving 0.5 + x = 0.977692361 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 = 0.977692361 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.977692361 + -0.5 x = 0.977692361 + -0.5 Combine like terms: 0.977692361 + -0.5 = 0.477692361 x = 0.477692361 Simplifying x = 0.477692361

Subproblem 2

x + 0.5 = -0.977692361 Simplifying x + 0.5 = -0.977692361 Reorder the terms: 0.5 + x = -0.977692361 Solving 0.5 + x = -0.977692361 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 = -0.977692361 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.977692361 + -0.5 x = -0.977692361 + -0.5 Combine like terms: -0.977692361 + -0.5 = -1.477692361 x = -1.477692361 Simplifying x = -1.477692361

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.477692361, -1.477692361}

Solution

x = {0.477692361, -1.477692361}

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