4(x+2)(3x-7)=22x-65

Simple and best practice solution for 4(x+2)(3x-7)=22x-65 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 4(x+2)(3x-7)=22x-65 equation:


Simplifying
4(x + 2)(3x + -7) = 22x + -65

Reorder the terms:
4(2 + x)(3x + -7) = 22x + -65

Reorder the terms:
4(2 + x)(-7 + 3x) = 22x + -65

Multiply (2 + x) * (-7 + 3x)
4(2(-7 + 3x) + x(-7 + 3x)) = 22x + -65
4((-7 * 2 + 3x * 2) + x(-7 + 3x)) = 22x + -65
4((-14 + 6x) + x(-7 + 3x)) = 22x + -65
4(-14 + 6x + (-7 * x + 3x * x)) = 22x + -65
4(-14 + 6x + (-7x + 3x2)) = 22x + -65

Combine like terms: 6x + -7x = -1x
4(-14 + -1x + 3x2) = 22x + -65
(-14 * 4 + -1x * 4 + 3x2 * 4) = 22x + -65
(-56 + -4x + 12x2) = 22x + -65

Reorder the terms:
-56 + -4x + 12x2 = -65 + 22x

Solving
-56 + -4x + 12x2 = -65 + 22x

Solving for variable 'x'.

Reorder the terms:
-56 + 65 + -4x + -22x + 12x2 = -65 + 22x + 65 + -22x

Combine like terms: -56 + 65 = 9
9 + -4x + -22x + 12x2 = -65 + 22x + 65 + -22x

Combine like terms: -4x + -22x = -26x
9 + -26x + 12x2 = -65 + 22x + 65 + -22x

Reorder the terms:
9 + -26x + 12x2 = -65 + 65 + 22x + -22x

Combine like terms: -65 + 65 = 0
9 + -26x + 12x2 = 0 + 22x + -22x
9 + -26x + 12x2 = 22x + -22x

Combine like terms: 22x + -22x = 0
9 + -26x + 12x2 = 0

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

Divide each side by '12'.
0.75 + -2.166666667x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -2.166666667x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -2.166666667x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -2.166666667x + x2 = 0 + -0.75
-2.166666667x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-2.166666667x + x2 = -0.75

The x term is -2.166666667x.  Take half its coefficient (-1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
-2.166666667x + 1.173611113 + x2 = -0.75 + 1.173611113

Reorder the terms:
1.173611113 + -2.166666667x + x2 = -0.75 + 1.173611113

Combine like terms: -0.75 + 1.173611113 = 0.423611113
1.173611113 + -2.166666667x + x2 = 0.423611113

Factor a perfect square on the left side:
(x + -1.083333334)(x + -1.083333334) = 0.423611113

Calculate the square root of the right side: 0.650854141

Break this problem into two subproblems by setting 
(x + -1.083333334) equal to 0.650854141 and -0.650854141.

Subproblem 1

x + -1.083333334 = 0.650854141 Simplifying x + -1.083333334 = 0.650854141 Reorder the terms: -1.083333334 + x = 0.650854141 Solving -1.083333334 + x = 0.650854141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = 0.650854141 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = 0.650854141 + 1.083333334 x = 0.650854141 + 1.083333334 Combine like terms: 0.650854141 + 1.083333334 = 1.734187475 x = 1.734187475 Simplifying x = 1.734187475

Subproblem 2

x + -1.083333334 = -0.650854141 Simplifying x + -1.083333334 = -0.650854141 Reorder the terms: -1.083333334 + x = -0.650854141 Solving -1.083333334 + x = -0.650854141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = -0.650854141 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = -0.650854141 + 1.083333334 x = -0.650854141 + 1.083333334 Combine like terms: -0.650854141 + 1.083333334 = 0.432479193 x = 0.432479193 Simplifying x = 0.432479193

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.734187475, 0.432479193}

See similar equations:

| 54x^2+11x+54=0 | | n+6-9n+2= | | 8(6-3x)+2(-3x-4)=0 | | 5-7c=-3c-3 | | (5x^3-7x^2+5x)-(4x^2+2x+8)= | | -4x^2+5=0 | | 4p-5=15 | | 6+2.5=6 | | 6*sin(3x)=5 | | 0=ln(0+c) | | 2(3x+6)-3(-3x+5)=13(10-1) | | x^2+8x=950 | | C=85+0.5Y | | X-y+9z=-8 | | 4(x+2)=5(x+6)+2 | | 4x^4+3x^2-10=0 | | 4(x+2)=(x+6)+2 | | y=-0.04x^2+1.2x | | x^30=5 | | 2(4y-1)=3y | | 9x-n^2=180 | | A(x)=80x-2x^2 | | g(x)=3sin(x) | | -5x-11=30x+24 | | (2x-3)*(2x-3)=0 | | 28=4+(12+-0.5c)+c | | -(5x+14)-9=-3(2x-1)-7 | | 2x^2+10x-340=0 | | 5(x+6)=8(x+3)+2 | | 46=2y | | 51=3 | | 28=c+(a+2)+(a+2) |

Equations solver categories