3x(-4x+9)=-45

Simple and best practice solution for 3x(-4x+9)=-45 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 3x(-4x+9)=-45 equation: 


Simplifying
3x(-4x + 9) = -45

Reorder the terms:
3x(9 + -4x) = -45
(9 * 3x + -4x * 3x) = -45
(27x + -12x2) = -45

Solving
27x + -12x2 = -45

Solving for variable 'x'.

Reorder the terms:
45 + 27x + -12x2 = -45 + 45

Combine like terms: -45 + 45 = 0
45 + 27x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + 9x + -4x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(15 + 9x + -4x2)' equal to zero and attempt to solve:

Simplifying
15 + 9x + -4x2 = 0

Solving
15 + 9x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-3.75 + -2.25x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -2.25x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -2.25x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -2.25x + x2 = 0 + 3.75
-2.25x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-2.25x + x2 = 3.75

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = 3.75 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = 3.75 + 1.265625

Combine like terms: 3.75 + 1.265625 = 5.015625
1.265625 + -2.25x + x2 = 5.015625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 5.015625

Calculate the square root of the right side: 2.239559108

Break this problem into two subproblems by setting 
(x + -1.125) equal to 2.239559108 and -2.239559108.


Subproblem 1
x + -1.125 = 2.239559108

Simplifying
x + -1.125 = 2.239559108

Reorder the terms:
-1.125 + x = 2.239559108

Solving
-1.125 + x = 2.239559108

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = 2.239559108 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 2.239559108 + 1.125
x = 2.239559108 + 1.125

Combine like terms: 2.239559108 + 1.125 = 3.364559108
x = 3.364559108

Simplifying
x = 3.364559108


Subproblem 2
x + -1.125 = -2.239559108

Simplifying
x + -1.125 = -2.239559108

Reorder the terms:
-1.125 + x = -2.239559108

Solving
-1.125 + x = -2.239559108

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = -2.239559108 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -2.239559108 + 1.125
x = -2.239559108 + 1.125

Combine like terms: -2.239559108 + 1.125 = -1.114559108
x = -1.114559108

Simplifying
x = -1.114559108


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.364559108, -1.114559108}
Solution
x = {3.364559108, -1.114559108}

See similar equations:

| 3/4|8x–12|=6(X-1) | | x(x-1)(x+4)+12=0 | | 3x-14x-63=36 | | I=5*5 | | 3(tan(x))-7=1 | | I=25 | | 3/4|8x-12|=6(X-1) | | (4x^3)-20x=0 | | 13x+36=11x-98 | | 3x-4/5=10 | | 8a-4a=4a+6 | | 4x-7=2x+29 | | -3(6+5x)=-153 | | x/9-9=2 | | A=Brj | | -192=-6(8x+8) | | (-76)=4x+6(5x+27) | | 2x+19=-53+8x | | A=Bcy | | 14-7x+8x=-5-1 | | x^2-2x+1=60 | | c/11.25=1.25 | | 6x-5x-5=9 | | 8v^2-9v-1=0 | | 9x+8=15x | | 0=15x^3-x^2+3x-2 | | 17x-118=13x+94 | | n-7+4n= | | 2z-3y-8z+y=0 | | X-3=2x-15 | | 5x^8+175=0 | | 1/5x-1/7y |

Equations solver categories