3x^2-21x=-6x^2-5x-7

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Solution for 3x^2-21x=-6x^2-5x-7 equation: 


Simplifying
3x2 + -21x = -6x2 + -5x + -7

Reorder the terms:
-21x + 3x2 = -6x2 + -5x + -7

Reorder the terms:
-21x + 3x2 = -7 + -5x + -6x2

Solving
-21x + 3x2 = -7 + -5x + -6x2

Solving for variable 'x'.

Reorder the terms:
7 + -21x + 5x + 3x2 + 6x2 = -7 + -5x + -6x2 + 7 + 5x + 6x2

Combine like terms: -21x + 5x = -16x
7 + -16x + 3x2 + 6x2 = -7 + -5x + -6x2 + 7 + 5x + 6x2

Combine like terms: 3x2 + 6x2 = 9x2
7 + -16x + 9x2 = -7 + -5x + -6x2 + 7 + 5x + 6x2

Reorder the terms:
7 + -16x + 9x2 = -7 + 7 + -5x + 5x + -6x2 + 6x2

Combine like terms: -7 + 7 = 0
7 + -16x + 9x2 = 0 + -5x + 5x + -6x2 + 6x2
7 + -16x + 9x2 = -5x + 5x + -6x2 + 6x2

Combine like terms: -5x + 5x = 0
7 + -16x + 9x2 = 0 + -6x2 + 6x2
7 + -16x + 9x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
7 + -16x + 9x2 = 0

Factor a trinomial.
(7 + -9x)(1 + -1x) = 0


Subproblem 1
Set the factor '(7 + -9x)' equal to zero and attempt to solve:

Simplifying
7 + -9x = 0

Solving
7 + -9x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -9x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -9x = 0 + -7
-9x = 0 + -7

Combine like terms: 0 + -7 = -7
-9x = -7

Divide each side by '-9'.
x = 0.7777777778

Simplifying
x = 0.7777777778

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {0.7777777778, 1}

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