3x^2-42x+12=0

Simple and best practice solution for 3x^2-42x+12=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 3x^2-42x+12=0 equation: 


Simplifying
3x2 + -42x + 12 = 0

Reorder the terms:
12 + -42x + 3x2 = 0

Solving
12 + -42x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -14x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(4 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
4 + -14x + x2 = 0

Solving
4 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -14x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -14x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -14x + x2 = 0 + -4
-14x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-14x + x2 = -4

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -4 + 49

Reorder the terms:
49 + -14x + x2 = -4 + 49

Combine like terms: -4 + 49 = 45
49 + -14x + x2 = 45

Factor a perfect square on the left side:
(x + -7)(x + -7) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + -7) equal to 6.708203933 and -6.708203933.


Subproblem 1
x + -7 = 6.708203933

Simplifying
x + -7 = 6.708203933

Reorder the terms:
-7 + x = 6.708203933

Solving
-7 + x = 6.708203933

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 6.708203933 + 7

Combine like terms: -7 + 7 = 0
0 + x = 6.708203933 + 7
x = 6.708203933 + 7

Combine like terms: 6.708203933 + 7 = 13.708203933
x = 13.708203933

Simplifying
x = 13.708203933


Subproblem 2
x + -7 = -6.708203933

Simplifying
x + -7 = -6.708203933

Reorder the terms:
-7 + x = -6.708203933

Solving
-7 + x = -6.708203933

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -6.708203933 + 7

Combine like terms: -7 + 7 = 0
0 + x = -6.708203933 + 7
x = -6.708203933 + 7

Combine like terms: -6.708203933 + 7 = 0.291796067
x = 0.291796067

Simplifying
x = 0.291796067


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.708203933, 0.291796067}
Solution
x = {13.708203933, 0.291796067}

See similar equations:

| 7x+2(-5x-4)=2-8x | | 7(-3)-(-5)= | | 14=6(y+2)-8y | | 3+2b=-15 | | -77x+-14y=13 | | 3v-2=-10 | | -3n+2=-10 | | 3+2x+4x=9 | | -6-7+3x=2-4x+5 | | -6-73x=2-4x+5 | | -77x-2y=-13 | | -3+2=-10 | | -2x+4-x=22 | | 36x^2+18x=40 | | 3q+7=14 | | -3-2k=17 | | 6ax-2a+5x=13ax-2 | | 1-3r=10 | | (-3)(-2)(4)(-5)= | | 8x=-18-12x | | 8x=-18-12 | | 900=20(10+20x) | | -(-4)(-5)(1)= | | 10=.25(x-12) | | f(-9)=4x+1 | | 6y+16=8y | | .5(4x+5)=-6 | | 9x-5=3x+19-1 | | 12*(-4)= | | 3y+12=9y | | 14+3-15-10= | | 0*(-10)= |

Equations solver categories