(2x+5)(6x-1)=90

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Solution for (2x+5)(6x-1)=90 equation:


Simplifying
(2x + 5)(6x + -1) = 90

Reorder the terms:
(5 + 2x)(6x + -1) = 90

Reorder the terms:
(5 + 2x)(-1 + 6x) = 90

Multiply (5 + 2x) * (-1 + 6x)
(5(-1 + 6x) + 2x * (-1 + 6x)) = 90
((-1 * 5 + 6x * 5) + 2x * (-1 + 6x)) = 90
((-5 + 30x) + 2x * (-1 + 6x)) = 90
(-5 + 30x + (-1 * 2x + 6x * 2x)) = 90
(-5 + 30x + (-2x + 12x2)) = 90

Combine like terms: 30x + -2x = 28x
(-5 + 28x + 12x2) = 90

Solving
-5 + 28x + 12x2 = 90

Solving for variable 'x'.

Reorder the terms:
-5 + -90 + 28x + 12x2 = 90 + -90

Combine like terms: -5 + -90 = -95
-95 + 28x + 12x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-95 + 28x + 12x2 = 0

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

Divide each side by '12'.
-7.916666667 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '7.916666667' to each side of the equation.
-7.916666667 + 2.333333333x + 7.916666667 + x2 = 0 + 7.916666667

Reorder the terms:
-7.916666667 + 7.916666667 + 2.333333333x + x2 = 0 + 7.916666667

Combine like terms: -7.916666667 + 7.916666667 = 0.000000000
0.000000000 + 2.333333333x + x2 = 0 + 7.916666667
2.333333333x + x2 = 0 + 7.916666667

Combine like terms: 0 + 7.916666667 = 7.916666667
2.333333333x + x2 = 7.916666667

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 7.916666667 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 7.916666667 + 1.361111112

Combine like terms: 7.916666667 + 1.361111112 = 9.277777779
1.361111112 + 2.333333333x + x2 = 9.277777779

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 9.277777779

Calculate the square root of the right side: 3.045944481

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 3.045944481 and -3.045944481.

Subproblem 1

x + 1.166666667 = 3.045944481 Simplifying x + 1.166666667 = 3.045944481 Reorder the terms: 1.166666667 + x = 3.045944481 Solving 1.166666667 + x = 3.045944481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 3.045944481 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 3.045944481 + -1.166666667 x = 3.045944481 + -1.166666667 Combine like terms: 3.045944481 + -1.166666667 = 1.879277814 x = 1.879277814 Simplifying x = 1.879277814

Subproblem 2

x + 1.166666667 = -3.045944481 Simplifying x + 1.166666667 = -3.045944481 Reorder the terms: 1.166666667 + x = -3.045944481 Solving 1.166666667 + x = -3.045944481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -3.045944481 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -3.045944481 + -1.166666667 x = -3.045944481 + -1.166666667 Combine like terms: -3.045944481 + -1.166666667 = -4.212611148 x = -4.212611148 Simplifying x = -4.212611148

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.879277814, -4.212611148}

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