4x^2-x+12=6x+9

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Solution for 4x^2-x+12=6x+9 equation: 


Simplifying
4x2 + -1x + 12 = 6x + 9

Reorder the terms:
12 + -1x + 4x2 = 6x + 9

Reorder the terms:
12 + -1x + 4x2 = 9 + 6x

Solving
12 + -1x + 4x2 = 9 + 6x

Solving for variable 'x'.

Reorder the terms:
12 + -9 + -1x + -6x + 4x2 = 9 + 6x + -9 + -6x

Combine like terms: 12 + -9 = 3
3 + -1x + -6x + 4x2 = 9 + 6x + -9 + -6x

Combine like terms: -1x + -6x = -7x
3 + -7x + 4x2 = 9 + 6x + -9 + -6x

Reorder the terms:
3 + -7x + 4x2 = 9 + -9 + 6x + -6x

Combine like terms: 9 + -9 = 0
3 + -7x + 4x2 = 0 + 6x + -6x
3 + -7x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
3 + -7x + 4x2 = 0

Factor a trinomial.
(3 + -4x)(1 + -1x) = 0


Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75

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 = {0.75, 1}

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