6a+4(3a-7)=a(2a-5)

Simple and best practice solution for 6a+4(3a-7)=a(2a-5) 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 6a+4(3a-7)=a(2a-5) equation:


Simplifying
6a + 4(3a + -7) = a(2a + -5)

Reorder the terms:
6a + 4(-7 + 3a) = a(2a + -5)
6a + (-7 * 4 + 3a * 4) = a(2a + -5)
6a + (-28 + 12a) = a(2a + -5)

Reorder the terms:
-28 + 6a + 12a = a(2a + -5)

Combine like terms: 6a + 12a = 18a
-28 + 18a = a(2a + -5)

Reorder the terms:
-28 + 18a = a(-5 + 2a)
-28 + 18a = (-5 * a + 2a * a)
-28 + 18a = (-5a + 2a2)

Solving
-28 + 18a = -5a + 2a2

Solving for variable 'a'.

Combine like terms: 18a + 5a = 23a
-28 + 23a + -2a2 = -5a + 2a2 + 5a + -2a2

Reorder the terms:
-28 + 23a + -2a2 = -5a + 5a + 2a2 + -2a2

Combine like terms: -5a + 5a = 0
-28 + 23a + -2a2 = 0 + 2a2 + -2a2
-28 + 23a + -2a2 = 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
-28 + 23a + -2a2 = 0

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

Divide each side by '-2'.
14 + -11.5a + a2 = 0

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -11.5a + -14 + a2 = 0 + -14

Reorder the terms:
14 + -14 + -11.5a + a2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -11.5a + a2 = 0 + -14
-11.5a + a2 = 0 + -14

Combine like terms: 0 + -14 = -14
-11.5a + a2 = -14

The a term is -11.5a.  Take half its coefficient (-5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
-11.5a + 33.0625 + a2 = -14 + 33.0625

Reorder the terms:
33.0625 + -11.5a + a2 = -14 + 33.0625

Combine like terms: -14 + 33.0625 = 19.0625
33.0625 + -11.5a + a2 = 19.0625

Factor a perfect square on the left side:
(a + -5.75)(a + -5.75) = 19.0625

Calculate the square root of the right side: 4.366062299

Break this problem into two subproblems by setting 
(a + -5.75) equal to 4.366062299 and -4.366062299.

Subproblem 1

a + -5.75 = 4.366062299 Simplifying a + -5.75 = 4.366062299 Reorder the terms: -5.75 + a = 4.366062299 Solving -5.75 + a = 4.366062299 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + a = 4.366062299 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + a = 4.366062299 + 5.75 a = 4.366062299 + 5.75 Combine like terms: 4.366062299 + 5.75 = 10.116062299 a = 10.116062299 Simplifying a = 10.116062299

Subproblem 2

a + -5.75 = -4.366062299 Simplifying a + -5.75 = -4.366062299 Reorder the terms: -5.75 + a = -4.366062299 Solving -5.75 + a = -4.366062299 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + a = -4.366062299 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + a = -4.366062299 + 5.75 a = -4.366062299 + 5.75 Combine like terms: -4.366062299 + 5.75 = 1.383937701 a = 1.383937701 Simplifying a = 1.383937701

Solution

The solution to the problem is based on the solutions from the subproblems. a = {10.116062299, 1.383937701}

See similar equations:

| -34+t=19 | | 5x+-29=-19 | | 7x-4y=5 | | -12+d=14 | | -15+u=-23 | | 3x+7=73 | | 2x+2=y | | 5[7-(8x-5)]+9x=0 | | 18+t=-2 | | 53-5x=4x+18 | | x^2-4x-12y=32 | | x+8=44 | | y=4x^2-6x+5 | | 2a+5b=100 | | 1.4x+2.6=15.2 | | 216=2(5w)+(2w) | | 5bk+25bk-250k=0 | | x^2+(m+3)x+m=0 | | 5(4d-2)=d+5 | | x^2+2x-2=10 | | x^2+2x-2=-2 | | x^2+(m-3)x+m=0 | | 2vm^2-14vm=0 | | -24=-2x+4(x-8) | | 31-13+5w=28 | | 3x^2-7x+5m-3=0 | | 6x^2+57x=30 | | 9r-11-2r=59 | | 9r-112r=59 | | y=x^2+7x+6 | | 6+(-11)= | | 3m^2+16m+5= |

Equations solver categories