(2x+5)(x-4)=6

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Solution for (2x+5)(x-4)=6 equation:


Simplifying
(2x + 5)(x + -4) = 6

Reorder the terms:
(5 + 2x)(x + -4) = 6

Reorder the terms:
(5 + 2x)(-4 + x) = 6

Multiply (5 + 2x) * (-4 + x)
(5(-4 + x) + 2x * (-4 + x)) = 6
((-4 * 5 + x * 5) + 2x * (-4 + x)) = 6
((-20 + 5x) + 2x * (-4 + x)) = 6
(-20 + 5x + (-4 * 2x + x * 2x)) = 6
(-20 + 5x + (-8x + 2x2)) = 6

Combine like terms: 5x + -8x = -3x
(-20 + -3x + 2x2) = 6

Solving
-20 + -3x + 2x2 = 6

Solving for variable 'x'.

Reorder the terms:
-20 + -6 + -3x + 2x2 = 6 + -6

Combine like terms: -20 + -6 = -26
-26 + -3x + 2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-26 + -3x + 2x2 = 0

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

Divide each side by '2'.
-13 + -1.5x + x2 = 0

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -1.5x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + -1.5x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1.5x + x2 = 0 + 13
-1.5x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
-1.5x + x2 = 13

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 13 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 13 + 0.5625

Combine like terms: 13 + 0.5625 = 13.5625
0.5625 + -1.5x + x2 = 13.5625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 13.5625

Calculate the square root of the right side: 3.682729966

Break this problem into two subproblems by setting 
(x + -0.75) equal to 3.682729966 and -3.682729966.

Subproblem 1

x + -0.75 = 3.682729966 Simplifying x + -0.75 = 3.682729966 Reorder the terms: -0.75 + x = 3.682729966 Solving -0.75 + x = 3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 3.682729966 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 3.682729966 + 0.75 x = 3.682729966 + 0.75 Combine like terms: 3.682729966 + 0.75 = 4.432729966 x = 4.432729966 Simplifying x = 4.432729966

Subproblem 2

x + -0.75 = -3.682729966 Simplifying x + -0.75 = -3.682729966 Reorder the terms: -0.75 + x = -3.682729966 Solving -0.75 + x = -3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -3.682729966 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -3.682729966 + 0.75 x = -3.682729966 + 0.75 Combine like terms: -3.682729966 + 0.75 = -2.932729966 x = -2.932729966 Simplifying x = -2.932729966

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.432729966, -2.932729966}

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