0=4x^2+19x-54

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Solution for 0=4x^2+19x-54 equation:


Simplifying
0 = 4x2 + 19x + -54

Reorder the terms:
0 = -54 + 19x + 4x2

Solving
0 = -54 + 19x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 54 = 54
54 + -19x + -4x2 = -54 + 19x + 4x2 + 54 + -19x + -4x2

Reorder the terms:
54 + -19x + -4x2 = -54 + 54 + 19x + -19x + 4x2 + -4x2

Combine like terms: -54 + 54 = 0
54 + -19x + -4x2 = 0 + 19x + -19x + 4x2 + -4x2
54 + -19x + -4x2 = 19x + -19x + 4x2 + -4x2

Combine like terms: 19x + -19x = 0
54 + -19x + -4x2 = 0 + 4x2 + -4x2
54 + -19x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
54 + -19x + -4x2 = 0

Factor a trinomial.
(2 + -1x)(27 + 4x) = 0

Subproblem 1

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Subproblem 2

Set the factor '(27 + 4x)' equal to zero and attempt to solve: Simplifying 27 + 4x = 0 Solving 27 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + 4x = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 4x = 0 + -27 4x = 0 + -27 Combine like terms: 0 + -27 = -27 4x = -27 Divide each side by '4'. x = -6.75 Simplifying x = -6.75

Solution

x = {2, -6.75}

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