(0.5x-3)(0.6x+3)=0

Simple and best practice solution for (0.5x-3)(0.6x+3)=0 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 (0.5x-3)(0.6x+3)=0 equation:


Simplifying
(0.5x + -3)(0.6x + 3) = 0

Reorder the terms:
(-3 + 0.5x)(0.6x + 3) = 0

Reorder the terms:
(-3 + 0.5x)(3 + 0.6x) = 0

Multiply (-3 + 0.5x) * (3 + 0.6x)
(-3(3 + 0.6x) + 0.5x * (3 + 0.6x)) = 0
((3 * -3 + 0.6x * -3) + 0.5x * (3 + 0.6x)) = 0
((-9 + -1.8x) + 0.5x * (3 + 0.6x)) = 0
(-9 + -1.8x + (3 * 0.5x + 0.6x * 0.5x)) = 0
(-9 + -1.8x + (1.5x + 0.3x2)) = 0

Combine like terms: -1.8x + 1.5x = -0.3x
(-9 + -0.3x + 0.3x2) = 0

Solving
-9 + -0.3x + 0.3x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.3'.
-30 + -1x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -1x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -1x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -1x + x2 = 0 + 30
-1x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-1x + x2 = 30

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 30 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 30 + 0.25

Combine like terms: 30 + 0.25 = 30.25
0.25 + -1x + x2 = 30.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 30.25

Calculate the square root of the right side: 5.5

Break this problem into two subproblems by setting 
(x + -0.5) equal to 5.5 and -5.5.

Subproblem 1

x + -0.5 = 5.5 Simplifying x + -0.5 = 5.5 Reorder the terms: -0.5 + x = 5.5 Solving -0.5 + x = 5.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 5.5 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.5 + 0.5 x = 5.5 + 0.5 Combine like terms: 5.5 + 0.5 = 6 x = 6 Simplifying x = 6

Subproblem 2

x + -0.5 = -5.5 Simplifying x + -0.5 = -5.5 Reorder the terms: -0.5 + x = -5.5 Solving -0.5 + x = -5.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -5.5 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.5 + 0.5 x = -5.5 + 0.5 Combine like terms: -5.5 + 0.5 = -5 x = -5 Simplifying x = -5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6, -5}

See similar equations:

| 27k+(-24k)=24 | | 7x-7=9x-3x | | 5x+7=-7 | | 16.1=5x+5.6 | | (x-3)*(x-2)=q | | -4a-50a+6a-(-31a)-(-13a)-17=19 | | x+(3-5x)=-9 | | 7x-1=7+5x | | 12(1)+3y=15 | | x+7*4=-3 | | 12(-1)+3y=15 | | (x-40)=87 | | 9p^2=12p | | 3y-5(4-y)=88 | | 13.6=8w+12 | | 9.8+c-9.8=3.6+9.8 | | y=x^3-x^2-px+q | | 8x-8=5x+13 | | 3x-37=15 | | -6+2+3x=29 | | x^3-x^2-px+q=0 | | 1+7z*z= | | 16x-192=m | | 16b-12b-b+5b=48 | | 10=18b+2.8 | | 5+6=6 | | 47j-37j=40 | | 12x-8=7x+12 | | 2.7+b+2.7=3.5+2.7 | | 4(-3)=7(x+2) | | 2x+17=6x-3 | | 2s+s-2s+5=29 |

Equations solver categories