3x^2-69x=-6x^2-7x-48

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Solution for 3x^2-69x=-6x^2-7x-48 equation: 


Simplifying
3x2 + -69x = -6x2 + -7x + -48

Reorder the terms:
-69x + 3x2 = -6x2 + -7x + -48

Reorder the terms:
-69x + 3x2 = -48 + -7x + -6x2

Solving
-69x + 3x2 = -48 + -7x + -6x2

Solving for variable 'x'.

Reorder the terms:
48 + -69x + 7x + 3x2 + 6x2 = -48 + -7x + -6x2 + 48 + 7x + 6x2

Combine like terms: -69x + 7x = -62x
48 + -62x + 3x2 + 6x2 = -48 + -7x + -6x2 + 48 + 7x + 6x2

Combine like terms: 3x2 + 6x2 = 9x2
48 + -62x + 9x2 = -48 + -7x + -6x2 + 48 + 7x + 6x2

Reorder the terms:
48 + -62x + 9x2 = -48 + 48 + -7x + 7x + -6x2 + 6x2

Combine like terms: -48 + 48 = 0
48 + -62x + 9x2 = 0 + -7x + 7x + -6x2 + 6x2
48 + -62x + 9x2 = -7x + 7x + -6x2 + 6x2

Combine like terms: -7x + 7x = 0
48 + -62x + 9x2 = 0 + -6x2 + 6x2
48 + -62x + 9x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
48 + -62x + 9x2 = 0

Factor a trinomial.
(8 + -9x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0.8888888889, 6}

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