(x+3)(2x+5)=42

Simple and best practice solution for (x+3)(2x+5)=42 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for (x+3)(2x+5)=42 equation:


Simplifying
(x + 3)(2x + 5) = 42

Reorder the terms:
(3 + x)(2x + 5) = 42

Reorder the terms:
(3 + x)(5 + 2x) = 42

Multiply (3 + x) * (5 + 2x)
(3(5 + 2x) + x(5 + 2x)) = 42
((5 * 3 + 2x * 3) + x(5 + 2x)) = 42
((15 + 6x) + x(5 + 2x)) = 42
(15 + 6x + (5 * x + 2x * x)) = 42
(15 + 6x + (5x + 2x2)) = 42

Combine like terms: 6x + 5x = 11x
(15 + 11x + 2x2) = 42

Solving
15 + 11x + 2x2 = 42

Solving for variable 'x'.

Reorder the terms:
15 + -42 + 11x + 2x2 = 42 + -42

Combine like terms: 15 + -42 = -27
-27 + 11x + 2x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-27 + 11x + 2x2 = 0

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

Divide each side by '2'.
-13.5 + 5.5x + x2 = 0

Move the constant term to the right:

Add '13.5' to each side of the equation.
-13.5 + 5.5x + 13.5 + x2 = 0 + 13.5

Reorder the terms:
-13.5 + 13.5 + 5.5x + x2 = 0 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + 5.5x + x2 = 0 + 13.5
5.5x + x2 = 0 + 13.5

Combine like terms: 0 + 13.5 = 13.5
5.5x + x2 = 13.5

The x term is 5.5x.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5x + 7.5625 + x2 = 13.5 + 7.5625

Reorder the terms:
7.5625 + 5.5x + x2 = 13.5 + 7.5625

Combine like terms: 13.5 + 7.5625 = 21.0625
7.5625 + 5.5x + x2 = 21.0625

Factor a perfect square on the left side:
(x + 2.75)(x + 2.75) = 21.0625

Calculate the square root of the right side: 4.589389938

Break this problem into two subproblems by setting 
(x + 2.75) equal to 4.589389938 and -4.589389938.

Subproblem 1

x + 2.75 = 4.589389938 Simplifying x + 2.75 = 4.589389938 Reorder the terms: 2.75 + x = 4.589389938 Solving 2.75 + x = 4.589389938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 4.589389938 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 4.589389938 + -2.75 x = 4.589389938 + -2.75 Combine like terms: 4.589389938 + -2.75 = 1.839389938 x = 1.839389938 Simplifying x = 1.839389938

Subproblem 2

x + 2.75 = -4.589389938 Simplifying x + 2.75 = -4.589389938 Reorder the terms: 2.75 + x = -4.589389938 Solving 2.75 + x = -4.589389938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -4.589389938 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -4.589389938 + -2.75 x = -4.589389938 + -2.75 Combine like terms: -4.589389938 + -2.75 = -7.339389938 x = -7.339389938 Simplifying x = -7.339389938

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.839389938, -7.339389938}

See similar equations:

| 0.57x=127.11 | | 5x+6=36-2x | | 4x+8=6x+5 | | 2(x-1)=1-(3-x) | | 6(1+y)7=17.18 | | P/6128=700/331 | | Y=600x+.32 | | 23-4x=5+3x | | 2xsquare+13x+15=42 | | 8y-2+15y-24=12y+6 | | x+2=137 | | X/36=8/9 | | 2x^2-27x+54=0 | | 1/3x=5/3 | | -2x+(x-7)=3x-(4+x) | | 2x^3-x^2+2x=0 | | 3/20=1/4x | | 4x^2+20=2 | | 4sin(2x)+3cos(2x)=0 | | (x+1)(x+1)-(x-2)(x-2)+(x+3)(x+3)=0 | | 20n+10=12n-6 | | 2xsquared+13x+15=42 | | 8n+4=4n-2 | | kq-9q+kr-9r=0 | | -4x^2+6x+4=0 | | y^2-6y=4x+3 | | 4x^2+20x=2 | | 7q/3p*7q | | -7(x-2)+1=15 | | 12w+20t=112 | | -0.0006(x)(x-200)=5 | | (x-6)(x-5+2i)(x-5-2i)=-636 |

Equations solver categories