0=4x^2-3x-27

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Solution for 0=4x^2-3x-27 equation: 


Simplifying
0 = 4x2 + -3x + -27

Reorder the terms:
0 = -27 + -3x + 4x2

Solving
0 = -27 + -3x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 27 = 27
27 + 3x + -4x2 = -27 + -3x + 4x2 + 27 + 3x + -4x2

Reorder the terms:
27 + 3x + -4x2 = -27 + 27 + -3x + 3x + 4x2 + -4x2

Combine like terms: -27 + 27 = 0
27 + 3x + -4x2 = 0 + -3x + 3x + 4x2 + -4x2
27 + 3x + -4x2 = -3x + 3x + 4x2 + -4x2

Combine like terms: -3x + 3x = 0
27 + 3x + -4x2 = 0 + 4x2 + -4x2
27 + 3x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
27 + 3x + -4x2 = 0

Factor a trinomial.
(3 + -1x)(9 + 4x) = 0


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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(9 + 4x)' equal to zero and attempt to solve:

Simplifying
9 + 4x = 0

Solving
9 + 4x = 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 + 4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4x = 0 + -9
4x = 0 + -9

Combine like terms: 0 + -9 = -9
4x = -9

Divide each side by '4'.
x = -2.25

Simplifying
x = -2.25
Solution
x = {3, -2.25}

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