(x-3)(5x-2)=(x-7)(x-3)

Simple and best practice solution for (x-3)(5x-2)=(x-7)(x-3) 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)(5x-2)=(x-7)(x-3) equation: 


Simplifying
(x + -3)(5x + -2) = (x + -7)(x + -3)

Reorder the terms:
(-3 + x)(5x + -2) = (x + -7)(x + -3)

Reorder the terms:
(-3 + x)(-2 + 5x) = (x + -7)(x + -3)

Multiply (-3 + x) * (-2 + 5x)
(-3(-2 + 5x) + x(-2 + 5x)) = (x + -7)(x + -3)
((-2 * -3 + 5x * -3) + x(-2 + 5x)) = (x + -7)(x + -3)
((6 + -15x) + x(-2 + 5x)) = (x + -7)(x + -3)
(6 + -15x + (-2 * x + 5x * x)) = (x + -7)(x + -3)
(6 + -15x + (-2x + 5x2)) = (x + -7)(x + -3)

Combine like terms: -15x + -2x = -17x
(6 + -17x + 5x2) = (x + -7)(x + -3)

Reorder the terms:
6 + -17x + 5x2 = (-7 + x)(x + -3)

Reorder the terms:
6 + -17x + 5x2 = (-7 + x)(-3 + x)

Multiply (-7 + x) * (-3 + x)
6 + -17x + 5x2 = (-7(-3 + x) + x(-3 + x))
6 + -17x + 5x2 = ((-3 * -7 + x * -7) + x(-3 + x))
6 + -17x + 5x2 = ((21 + -7x) + x(-3 + x))
6 + -17x + 5x2 = (21 + -7x + (-3 * x + x * x))
6 + -17x + 5x2 = (21 + -7x + (-3x + x2))

Combine like terms: -7x + -3x = -10x
6 + -17x + 5x2 = (21 + -10x + x2)

Solving
6 + -17x + 5x2 = 21 + -10x + x2

Solving for variable 'x'.

Reorder the terms:
6 + -21 + -17x + 10x + 5x2 + -1x2 = 21 + -10x + x2 + -21 + 10x + -1x2

Combine like terms: 6 + -21 = -15
-15 + -17x + 10x + 5x2 + -1x2 = 21 + -10x + x2 + -21 + 10x + -1x2

Combine like terms: -17x + 10x = -7x
-15 + -7x + 5x2 + -1x2 = 21 + -10x + x2 + -21 + 10x + -1x2

Combine like terms: 5x2 + -1x2 = 4x2
-15 + -7x + 4x2 = 21 + -10x + x2 + -21 + 10x + -1x2

Reorder the terms:
-15 + -7x + 4x2 = 21 + -21 + -10x + 10x + x2 + -1x2

Combine like terms: 21 + -21 = 0
-15 + -7x + 4x2 = 0 + -10x + 10x + x2 + -1x2
-15 + -7x + 4x2 = -10x + 10x + x2 + -1x2

Combine like terms: -10x + 10x = 0
-15 + -7x + 4x2 = 0 + x2 + -1x2
-15 + -7x + 4x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-15 + -7x + 4x2 = 0

Factor a trinomial.
(-5 + -4x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve:

Simplifying
-5 + -4x = 0

Solving
-5 + -4x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -4x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4x = 0 + 5
-4x = 0 + 5

Combine like terms: 0 + 5 = 5
-4x = 5

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1.25, 3}

See similar equations:

| .50x+0.25(50)=0.25(110) | | 22x+9=451-4x | | 25x-156=2x-18 | | 27x-29=203-2x | | .06(y-4)+0.12y=0.20y-0.01(10) | | 18x+24=9x+96 | | 10x+25=295-8x | | 16p-20q= | | 2a(3a+2)=34 | | 2x+14=-4+7x | | 20x+9=198-7x | | 100x-1=51 | | (225.40*X)/Y=39.04 | | 3(8a-10)=5(7a+5) | | (225,40*X)/Y=3904 | | (18+2y)(15+2x)=644 | | 3a(8a-10)=5(7a+5) | | 8(n-6)=7-6 | | 2x*(3x+2)=34 | | 5M/2(4) | | 2x(3x+2)=34 | | 6*R=54 | | 7(x-3)=3x+9 | | 7(y+3)-2(y-1)=0 | | 8*p=-32 | | sin^2(x)+2=7*cos(x) | | 1+1=32 | | 10x-2=12x+12 | | 7(f+1)=10f-21 | | 5(3x+3)=5(4x-4) | | 9/p=1 | | Fx=5-4x/15 |

Equations solver categories