(2a-5)(a-3)=1

Simple and best practice solution for (2a-5)(a-3)=1 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 (2a-5)(a-3)=1 equation: 


Simplifying
(2a + -5)(a + -3) = 1

Reorder the terms:
(-5 + 2a)(a + -3) = 1

Reorder the terms:
(-5 + 2a)(-3 + a) = 1

Multiply (-5 + 2a) * (-3 + a)
(-5(-3 + a) + 2a * (-3 + a)) = 1
((-3 * -5 + a * -5) + 2a * (-3 + a)) = 1
((15 + -5a) + 2a * (-3 + a)) = 1
(15 + -5a + (-3 * 2a + a * 2a)) = 1
(15 + -5a + (-6a + 2a2)) = 1

Combine like terms: -5a + -6a = -11a
(15 + -11a + 2a2) = 1

Solving
15 + -11a + 2a2 = 1

Solving for variable 'a'.

Reorder the terms:
15 + -1 + -11a + 2a2 = 1 + -1

Combine like terms: 15 + -1 = 14
14 + -11a + 2a2 = 1 + -1

Combine like terms: 1 + -1 = 0
14 + -11a + 2a2 = 0

Factor a trinomial.
(2 + -1a)(7 + -2a) = 0


Subproblem 1
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2

Subproblem 2
Set the factor '(7 + -2a)' equal to zero and attempt to solve:

Simplifying
7 + -2a = 0

Solving
7 + -2a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -2a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2a = 0 + -7
-2a = 0 + -7

Combine like terms: 0 + -7 = -7
-2a = -7

Divide each side by '-2'.
a = 3.5

Simplifying
a = 3.5
Solution
a = {2, 3.5}

See similar equations:

| 71=11x-20x-1 | | y=2x^3-6x+1 | | 1+3c=13 | | 6a-7=3+a | | -22.5=-7x-5 | | A^2-3600=0 | | 5x+2(x+10)=-50 | | -22=2+3x | | 3x+y-21=0 2x+5y-y=0 | | 4(x-12)=5(x+1) | | 6x^2-1x-5=0 | | 8=4+2m | | 9.14*12=2x+2x^2 | | 1.23x=-4.192-2.77x | | -43=-8+5v | | 2(x+4)=-2(8x-1)+8x | | 10+sqrt(x-8)=x | | 4(3x+5)=7(x+3)-8 | | 14=1-6x-5 | | n/3–16=-14 | | 8+5(1-9k)=32 | | 8y+16=3y+50 | | 2x^2+4x+4=60 | | 10x-3x-1=0 | | 9x^2-0x-16= | | 1/3k=3/5 | | 5a-3(a-1)=17 | | 15b+39=105 | | r/12=1/3 | | r/12=11/3 | | (x^5)-3x+1=0 | | 7x^2+7x-14= |

Equations solver categories