2(x+5)*3(x-3)=26

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Solution for 2(x+5)*3(x-3)=26 equation:


Simplifying
2(x + 5) * 3(x + -3) = 26

Reorder the terms:
2(5 + x) * 3(x + -3) = 26

Reorder the terms:
2(5 + x) * 3(-3 + x) = 26

Reorder the terms for easier multiplication:
2 * 3(5 + x)(-3 + x) = 26

Multiply 2 * 3
6(5 + x)(-3 + x) = 26

Multiply (5 + x) * (-3 + x)
6(5(-3 + x) + x(-3 + x)) = 26
6((-3 * 5 + x * 5) + x(-3 + x)) = 26
6((-15 + 5x) + x(-3 + x)) = 26
6(-15 + 5x + (-3 * x + x * x)) = 26
6(-15 + 5x + (-3x + x2)) = 26

Combine like terms: 5x + -3x = 2x
6(-15 + 2x + x2) = 26
(-15 * 6 + 2x * 6 + x2 * 6) = 26
(-90 + 12x + 6x2) = 26

Solving
-90 + 12x + 6x2 = 26

Solving for variable 'x'.

Reorder the terms:
-90 + -26 + 12x + 6x2 = 26 + -26

Combine like terms: -90 + -26 = -116
-116 + 12x + 6x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-116 + 12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-58 + 6x + 3x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-58 + 6x + 3x2)' equal to zero and attempt to solve: Simplifying -58 + 6x + 3x2 = 0 Solving -58 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -19.33333333 + 2x + x2 = 0 Move the constant term to the right: Add '19.33333333' to each side of the equation. -19.33333333 + 2x + 19.33333333 + x2 = 0 + 19.33333333 Reorder the terms: -19.33333333 + 19.33333333 + 2x + x2 = 0 + 19.33333333 Combine like terms: -19.33333333 + 19.33333333 = 0.00000000 0.00000000 + 2x + x2 = 0 + 19.33333333 2x + x2 = 0 + 19.33333333 Combine like terms: 0 + 19.33333333 = 19.33333333 2x + x2 = 19.33333333 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 = 19.33333333 + 1 Reorder the terms: 1 + 2x + x2 = 19.33333333 + 1 Combine like terms: 19.33333333 + 1 = 20.33333333 1 + 2x + x2 = 20.33333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 20.33333333 Calculate the square root of the right side: 4.509249752 Break this problem into two subproblems by setting (x + 1) equal to 4.509249752 and -4.509249752.

Subproblem 1

x + 1 = 4.509249752 Simplifying x + 1 = 4.509249752 Reorder the terms: 1 + x = 4.509249752 Solving 1 + x = 4.509249752 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 = 4.509249752 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.509249752 + -1 x = 4.509249752 + -1 Combine like terms: 4.509249752 + -1 = 3.509249752 x = 3.509249752 Simplifying x = 3.509249752

Subproblem 2

x + 1 = -4.509249752 Simplifying x + 1 = -4.509249752 Reorder the terms: 1 + x = -4.509249752 Solving 1 + x = -4.509249752 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 = -4.509249752 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.509249752 + -1 x = -4.509249752 + -1 Combine like terms: -4.509249752 + -1 = -5.509249752 x = -5.509249752 Simplifying x = -5.509249752

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.509249752, -5.509249752}

Solution

x = {3.509249752, -5.509249752}

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