4x^2-21x-18=12x+9

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Solution for 4x^2-21x-18=12x+9 equation: 


Simplifying
4x2 + -21x + -18 = 12x + 9

Reorder the terms:
-18 + -21x + 4x2 = 12x + 9

Reorder the terms:
-18 + -21x + 4x2 = 9 + 12x

Solving
-18 + -21x + 4x2 = 9 + 12x

Solving for variable 'x'.

Reorder the terms:
-18 + -9 + -21x + -12x + 4x2 = 9 + 12x + -9 + -12x

Combine like terms: -18 + -9 = -27
-27 + -21x + -12x + 4x2 = 9 + 12x + -9 + -12x

Combine like terms: -21x + -12x = -33x
-27 + -33x + 4x2 = 9 + 12x + -9 + -12x

Reorder the terms:
-27 + -33x + 4x2 = 9 + -9 + 12x + -12x

Combine like terms: 9 + -9 = 0
-27 + -33x + 4x2 = 0 + 12x + -12x
-27 + -33x + 4x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-27 + -33x + 4x2 = 0

Factor a trinomial.
(-3 + -4x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-0.75, 9}

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