-2(4a+5)3a=18

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Solution for -2(4a+5)3a=18 equation:


Simplifying
-2(4a + 5) * 3a = 18

Reorder the terms:
-2(5 + 4a) * 3a = 18

Reorder the terms for easier multiplication:
-2 * 3a(5 + 4a) = 18

Multiply -2 * 3
-6a(5 + 4a) = 18
(5 * -6a + 4a * -6a) = 18
(-30a + -24a2) = 18

Solving
-30a + -24a2 = 18

Solving for variable 'a'.

Reorder the terms:
-18 + -30a + -24a2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + -30a + -24a2 = 0

Factor out the Greatest Common Factor (GCF), '-6'.
-6(3 + 5a + 4a2) = 0

Ignore the factor -6.

Subproblem 1
Set the factor '(3 + 5a + 4a2)' equal to zero and attempt to solve:

Simplifying
3 + 5a + 4a2 = 0

Solving
3 + 5a + 4a2 = 0

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

Divide each side by '4'.
0.75 + 1.25a + a2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 1.25a + -0.75 + a2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 1.25a + a2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 1.25a + a2 = 0 + -0.75
1.25a + a2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
1.25a + a2 = -0.75

The a term is 1.25a.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25a + 0.390625 + a2 = -0.75 + 0.390625

Reorder the terms:
0.390625 + 1.25a + a2 = -0.75 + 0.390625

Combine like terms: -0.75 + 0.390625 = -0.359375
0.390625 + 1.25a + a2 = -0.359375

Factor a perfect square on the left side:
(a + 0.625)(a + 0.625) = -0.359375

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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