3x(3+2x)+18=-24

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Solution for 3x(3+2x)+18=-24 equation: 


Simplifying
3x(3 + 2x) + 18 = -24
(3 * 3x + 2x * 3x) + 18 = -24
(9x + 6x2) + 18 = -24

Reorder the terms:
18 + 9x + 6x2 = -24

Solving
18 + 9x + 6x2 = -24

Solving for variable 'x'.

Reorder the terms:
18 + 24 + 9x + 6x2 = -24 + 24

Combine like terms: 18 + 24 = 42
42 + 9x + 6x2 = -24 + 24

Combine like terms: -24 + 24 = 0
42 + 9x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(14 + 3x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(14 + 3x + 2x2)' equal to zero and attempt to solve:

Simplifying
14 + 3x + 2x2 = 0

Solving
14 + 3x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
7 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 1.5x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 1.5x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 1.5x + x2 = 0 + -7
1.5x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
1.5x + x2 = -7

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = -7 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -7 + 0.5625

Combine like terms: -7 + 0.5625 = -6.4375
0.5625 + 1.5x + x2 = -6.4375

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = -6.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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