(2x+4)(3x)=180

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Solution for (2x+4)(3x)=180 equation:


Simplifying
(2x + 4)(3x) = 180

Reorder the terms:
(4 + 2x)(3x) = 180

Remove parenthesis around (3x)
(4 + 2x) * 3x = 180

Reorder the terms for easier multiplication:
3x(4 + 2x) = 180
(4 * 3x + 2x * 3x) = 180
(12x + 6x2) = 180

Solving
12x + 6x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 12x + 6x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-30 + 2x + x2) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-30 + 2x + x2)' equal to zero and attempt to solve: Simplifying -30 + 2x + x2 = 0 Solving -30 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 2x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 2x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 2x + x2 = 0 + 30 2x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 2x + x2 = 30 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 30 + 1 Reorder the terms: 1 + 2x + x2 = 30 + 1 Combine like terms: 30 + 1 = 31 1 + 2x + x2 = 31 Factor a perfect square on the left side: (x + 1)(x + 1) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + 1) equal to 5.567764363 and -5.567764363.

Subproblem 1

x + 1 = 5.567764363 Simplifying x + 1 = 5.567764363 Reorder the terms: 1 + x = 5.567764363 Solving 1 + x = 5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.567764363 + -1 x = 5.567764363 + -1 Combine like terms: 5.567764363 + -1 = 4.567764363 x = 4.567764363 Simplifying x = 4.567764363

Subproblem 2

x + 1 = -5.567764363 Simplifying x + 1 = -5.567764363 Reorder the terms: 1 + x = -5.567764363 Solving 1 + x = -5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.567764363 + -1 x = -5.567764363 + -1 Combine like terms: -5.567764363 + -1 = -6.567764363 x = -6.567764363 Simplifying x = -6.567764363

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.567764363, -6.567764363}

Solution

x = {4.567764363, -6.567764363}

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