(2+4x)*(3x-9)=18

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Solution for (2+4x)*(3x-9)=18 equation:


Simplifying
(2 + 4x)(3x + -9) = 18

Reorder the terms:
(2 + 4x)(-9 + 3x) = 18

Multiply (2 + 4x) * (-9 + 3x)
(2(-9 + 3x) + 4x * (-9 + 3x)) = 18
((-9 * 2 + 3x * 2) + 4x * (-9 + 3x)) = 18
((-18 + 6x) + 4x * (-9 + 3x)) = 18
(-18 + 6x + (-9 * 4x + 3x * 4x)) = 18
(-18 + 6x + (-36x + 12x2)) = 18

Combine like terms: 6x + -36x = -30x
(-18 + -30x + 12x2) = 18

Solving
-18 + -30x + 12x2 = 18

Solving for variable 'x'.

Reorder the terms:
-18 + -18 + -30x + 12x2 = 18 + -18

Combine like terms: -18 + -18 = -36
-36 + -30x + 12x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-36 + -30x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-6 + -5x + 2x2) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-6 + -5x + 2x2)' equal to zero and attempt to solve: Simplifying -6 + -5x + 2x2 = 0 Solving -6 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + -2.5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -2.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -2.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2.5x + x2 = 0 + 3 -2.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -2.5x + x2 = 3 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 3 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 3 + 1.5625 Combine like terms: 3 + 1.5625 = 4.5625 1.5625 + -2.5x + x2 = 4.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (x + -1.25) equal to 2.136000936 and -2.136000936.

Subproblem 1

x + -1.25 = 2.136000936 Simplifying x + -1.25 = 2.136000936 Reorder the terms: -1.25 + x = 2.136000936 Solving -1.25 + x = 2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.136000936 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.136000936 + 1.25 x = 2.136000936 + 1.25 Combine like terms: 2.136000936 + 1.25 = 3.386000936 x = 3.386000936 Simplifying x = 3.386000936

Subproblem 2

x + -1.25 = -2.136000936 Simplifying x + -1.25 = -2.136000936 Reorder the terms: -1.25 + x = -2.136000936 Solving -1.25 + x = -2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.136000936 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.136000936 + 1.25 x = -2.136000936 + 1.25 Combine like terms: -2.136000936 + 1.25 = -0.886000936 x = -0.886000936 Simplifying x = -0.886000936

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.386000936, -0.886000936}

Solution

x = {3.386000936, -0.886000936}

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