0=6x^2+17x+12

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Solution for 0=6x^2+17x+12 equation:


Simplifying
0 = 6x2 + 17x + 12

Reorder the terms:
0 = 12 + 17x + 6x2

Solving
0 = 12 + 17x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + -12 = -12
-12 + -17x + -6x2 = 12 + 17x + 6x2 + -12 + -17x + -6x2

Reorder the terms:
-12 + -17x + -6x2 = 12 + -12 + 17x + -17x + 6x2 + -6x2

Combine like terms: 12 + -12 = 0
-12 + -17x + -6x2 = 0 + 17x + -17x + 6x2 + -6x2
-12 + -17x + -6x2 = 17x + -17x + 6x2 + -6x2

Combine like terms: 17x + -17x = 0
-12 + -17x + -6x2 = 0 + 6x2 + -6x2
-12 + -17x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-12 + -17x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 17x + 6x2) = 0

Factor a trinomial.
-1((3 + 2x)(4 + 3x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5

Subproblem 2

Set the factor '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Divide each side by '3'. x = -1.333333333 Simplifying x = -1.333333333

Solution

x = {-1.5, -1.333333333}

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