9x^2-3x+4=15-x

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Solution for 9x^2-3x+4=15-x equation: 


Simplifying
9x2 + -3x + 4 = 15 + -1x

Reorder the terms:
4 + -3x + 9x2 = 15 + -1x

Solving
4 + -3x + 9x2 = 15 + -1x

Solving for variable 'x'.

Reorder the terms:
4 + -15 + -3x + x + 9x2 = 15 + -1x + -15 + x

Combine like terms: 4 + -15 = -11
-11 + -3x + x + 9x2 = 15 + -1x + -15 + x

Combine like terms: -3x + x = -2x
-11 + -2x + 9x2 = 15 + -1x + -15 + x

Reorder the terms:
-11 + -2x + 9x2 = 15 + -15 + -1x + x

Combine like terms: 15 + -15 = 0
-11 + -2x + 9x2 = 0 + -1x + x
-11 + -2x + 9x2 = -1x + x

Combine like terms: -1x + x = 0
-11 + -2x + 9x2 = 0

Factor a trinomial.
(-1 + -1x)(11 + -9x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(11 + -9x)' equal to zero and attempt to solve:

Simplifying
11 + -9x = 0

Solving
11 + -9x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -9x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -9x = 0 + -11
-9x = 0 + -11

Combine like terms: 0 + -11 = -11
-9x = -11

Divide each side by '-9'.
x = 1.222222222

Simplifying
x = 1.222222222
Solution
x = {-1, 1.222222222}

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