3x^2-42x=-6x^2-7x-24

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Solution for 3x^2-42x=-6x^2-7x-24 equation: 


Simplifying
3x2 + -42x = -6x2 + -7x + -24

Reorder the terms:
-42x + 3x2 = -6x2 + -7x + -24

Reorder the terms:
-42x + 3x2 = -24 + -7x + -6x2

Solving
-42x + 3x2 = -24 + -7x + -6x2

Solving for variable 'x'.

Reorder the terms:
24 + -42x + 7x + 3x2 + 6x2 = -24 + -7x + -6x2 + 24 + 7x + 6x2

Combine like terms: -42x + 7x = -35x
24 + -35x + 3x2 + 6x2 = -24 + -7x + -6x2 + 24 + 7x + 6x2

Combine like terms: 3x2 + 6x2 = 9x2
24 + -35x + 9x2 = -24 + -7x + -6x2 + 24 + 7x + 6x2

Reorder the terms:
24 + -35x + 9x2 = -24 + 24 + -7x + 7x + -6x2 + 6x2

Combine like terms: -24 + 24 = 0
24 + -35x + 9x2 = 0 + -7x + 7x + -6x2 + 6x2
24 + -35x + 9x2 = -7x + 7x + -6x2 + 6x2

Combine like terms: -7x + 7x = 0
24 + -35x + 9x2 = 0 + -6x2 + 6x2
24 + -35x + 9x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
24 + -35x + 9x2 = 0

Factor a trinomial.
(8 + -9x)(3 + -1x) = 0


Subproblem 1
Set the factor '(8 + -9x)' equal to zero and attempt to solve:

Simplifying
8 + -9x = 0

Solving
8 + -9x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -9x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -9x = 0 + -8
-9x = 0 + -8

Combine like terms: 0 + -8 = -8
-9x = -8

Divide each side by '-9'.
x = 0.8888888889

Simplifying
x = 0.8888888889

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 = {0.8888888889, 3}

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