5(3x-8)1(4x+6)+3=

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Solution for 5(3x-8)1(4x+6)+3= equation:


Simplifying
5(3x + -8) * 1(4x + 6) + 3 = 0

Reorder the terms:
5(-8 + 3x) * 1(4x + 6) + 3 = 0

Reorder the terms:
5(-8 + 3x) * 1(6 + 4x) + 3 = 0

Reorder the terms for easier multiplication:
5 * 1(-8 + 3x)(6 + 4x) + 3 = 0

Multiply 5 * 1
5(-8 + 3x)(6 + 4x) + 3 = 0

Multiply (-8 + 3x) * (6 + 4x)
5(-8(6 + 4x) + 3x * (6 + 4x)) + 3 = 0
5((6 * -8 + 4x * -8) + 3x * (6 + 4x)) + 3 = 0
5((-48 + -32x) + 3x * (6 + 4x)) + 3 = 0
5(-48 + -32x + (6 * 3x + 4x * 3x)) + 3 = 0
5(-48 + -32x + (18x + 12x2)) + 3 = 0

Combine like terms: -32x + 18x = -14x
5(-48 + -14x + 12x2) + 3 = 0
(-48 * 5 + -14x * 5 + 12x2 * 5) + 3 = 0
(-240 + -70x + 60x2) + 3 = 0

Reorder the terms:
-240 + 3 + -70x + 60x2 = 0

Combine like terms: -240 + 3 = -237
-237 + -70x + 60x2 = 0

Solving
-237 + -70x + 60x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
60 the coefficient of the squared term: 

Divide each side by '60'.
-3.95 + -1.166666667x + x2 = 0.0

Move the constant term to the right:

Add '3.95' to each side of the equation.
-3.95 + -1.166666667x + 3.95 + x2 = 0.0 + 3.95

Reorder the terms:
-3.95 + 3.95 + -1.166666667x + x2 = 0.0 + 3.95

Combine like terms: -3.95 + 3.95 = 0.00
0.00 + -1.166666667x + x2 = 0.0 + 3.95
-1.166666667x + x2 = 0.0 + 3.95

Combine like terms: 0.0 + 3.95 = 3.95
-1.166666667x + x2 = 3.95

The x term is -1.166666667x.  Take half its coefficient (-0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
-1.166666667x + 0.3402777780 + x2 = 3.95 + 0.3402777780

Reorder the terms:
0.3402777780 + -1.166666667x + x2 = 3.95 + 0.3402777780

Combine like terms: 3.95 + 0.3402777780 = 4.290277778
0.3402777780 + -1.166666667x + x2 = 4.290277778

Factor a perfect square on the left side:
(x + -0.5833333335)(x + -0.5833333335) = 4.290277778

Calculate the square root of the right side: 2.071298573

Break this problem into two subproblems by setting 
(x + -0.5833333335) equal to 2.071298573 and -2.071298573.

Subproblem 1

x + -0.5833333335 = 2.071298573 Simplifying x + -0.5833333335 = 2.071298573 Reorder the terms: -0.5833333335 + x = 2.071298573 Solving -0.5833333335 + x = 2.071298573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = 2.071298573 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 2.071298573 + 0.5833333335 x = 2.071298573 + 0.5833333335 Combine like terms: 2.071298573 + 0.5833333335 = 2.6546319065 x = 2.6546319065 Simplifying x = 2.6546319065

Subproblem 2

x + -0.5833333335 = -2.071298573 Simplifying x + -0.5833333335 = -2.071298573 Reorder the terms: -0.5833333335 + x = -2.071298573 Solving -0.5833333335 + x = -2.071298573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = -2.071298573 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -2.071298573 + 0.5833333335 x = -2.071298573 + 0.5833333335 Combine like terms: -2.071298573 + 0.5833333335 = -1.4879652395 x = -1.4879652395 Simplifying x = -1.4879652395

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.6546319065, -1.4879652395}

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