0=3x^2+14x+15

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Solution for 0=3x^2+14x+15 equation:


Simplifying
0 = 3x2 + 14x + 15

Reorder the terms:
0 = 15 + 14x + 3x2

Solving
0 = 15 + 14x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -15 = -15
-15 + -14x + -3x2 = 15 + 14x + 3x2 + -15 + -14x + -3x2

Reorder the terms:
-15 + -14x + -3x2 = 15 + -15 + 14x + -14x + 3x2 + -3x2

Combine like terms: 15 + -15 = 0
-15 + -14x + -3x2 = 0 + 14x + -14x + 3x2 + -3x2
-15 + -14x + -3x2 = 14x + -14x + 3x2 + -3x2

Combine like terms: 14x + -14x = 0
-15 + -14x + -3x2 = 0 + 3x2 + -3x2
-15 + -14x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-15 + -14x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 14x + 3x2) = 0

Factor a trinomial.
-1((3 + x)(5 + 3x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Subproblem 2

Set the factor '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667

Solution

x = {-3, -1.666666667}

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