(4x-42)*(x+3)=55

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Solution for (4x-42)*(x+3)=55 equation:


Simplifying
(4x + -42)(x + 3) = 55

Reorder the terms:
(-42 + 4x)(x + 3) = 55

Reorder the terms:
(-42 + 4x)(3 + x) = 55

Multiply (-42 + 4x) * (3 + x)
(-42(3 + x) + 4x * (3 + x)) = 55
((3 * -42 + x * -42) + 4x * (3 + x)) = 55
((-126 + -42x) + 4x * (3 + x)) = 55
(-126 + -42x + (3 * 4x + x * 4x)) = 55
(-126 + -42x + (12x + 4x2)) = 55

Combine like terms: -42x + 12x = -30x
(-126 + -30x + 4x2) = 55

Solving
-126 + -30x + 4x2 = 55

Solving for variable 'x'.

Reorder the terms:
-126 + -55 + -30x + 4x2 = 55 + -55

Combine like terms: -126 + -55 = -181
-181 + -30x + 4x2 = 55 + -55

Combine like terms: 55 + -55 = 0
-181 + -30x + 4x2 = 0

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

Divide each side by '4'.
-45.25 + -7.5x + x2 = 0

Move the constant term to the right:

Add '45.25' to each side of the equation.
-45.25 + -7.5x + 45.25 + x2 = 0 + 45.25

Reorder the terms:
-45.25 + 45.25 + -7.5x + x2 = 0 + 45.25

Combine like terms: -45.25 + 45.25 = 0.00
0.00 + -7.5x + x2 = 0 + 45.25
-7.5x + x2 = 0 + 45.25

Combine like terms: 0 + 45.25 = 45.25
-7.5x + x2 = 45.25

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = 45.25 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = 45.25 + 14.0625

Combine like terms: 45.25 + 14.0625 = 59.3125
14.0625 + -7.5x + x2 = 59.3125

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 59.3125

Calculate the square root of the right side: 7.7014609

Break this problem into two subproblems by setting 
(x + -3.75) equal to 7.7014609 and -7.7014609.

Subproblem 1

x + -3.75 = 7.7014609 Simplifying x + -3.75 = 7.7014609 Reorder the terms: -3.75 + x = 7.7014609 Solving -3.75 + x = 7.7014609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 7.7014609 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 7.7014609 + 3.75 x = 7.7014609 + 3.75 Combine like terms: 7.7014609 + 3.75 = 11.4514609 x = 11.4514609 Simplifying x = 11.4514609

Subproblem 2

x + -3.75 = -7.7014609 Simplifying x + -3.75 = -7.7014609 Reorder the terms: -3.75 + x = -7.7014609 Solving -3.75 + x = -7.7014609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -7.7014609 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -7.7014609 + 3.75 x = -7.7014609 + 3.75 Combine like terms: -7.7014609 + 3.75 = -3.9514609 x = -3.9514609 Simplifying x = -3.9514609

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.4514609, -3.9514609}

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