45x^2+135x+62=-8

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Solution for 45x^2+135x+62=-8 equation: 


Simplifying
45x2 + 135x + 62 = -8

Reorder the terms:
62 + 135x + 45x2 = -8

Solving
62 + 135x + 45x2 = -8

Solving for variable 'x'.

Reorder the terms:
62 + 8 + 135x + 45x2 = -8 + 8

Combine like terms: 62 + 8 = 70
70 + 135x + 45x2 = -8 + 8

Combine like terms: -8 + 8 = 0
70 + 135x + 45x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(14 + 27x + 9x2) = 0

Factor a trinomial.
5((7 + 3x)(2 + 3x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333

Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {-2.333333333, -0.6666666667}

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