3a(4-5a)=2a+10

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Solution for 3a(4-5a)=2a+10 equation:


Simplifying
3a(4 + -5a) = 2a + 10
(4 * 3a + -5a * 3a) = 2a + 10
(12a + -15a2) = 2a + 10

Reorder the terms:
12a + -15a2 = 10 + 2a

Solving
12a + -15a2 = 10 + 2a

Solving for variable 'a'.

Reorder the terms:
-10 + 12a + -2a + -15a2 = 10 + 2a + -10 + -2a

Combine like terms: 12a + -2a = 10a
-10 + 10a + -15a2 = 10 + 2a + -10 + -2a

Reorder the terms:
-10 + 10a + -15a2 = 10 + -10 + 2a + -2a

Combine like terms: 10 + -10 = 0
-10 + 10a + -15a2 = 0 + 2a + -2a
-10 + 10a + -15a2 = 2a + -2a

Combine like terms: 2a + -2a = 0
-10 + 10a + -15a2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + 2a + -3a2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-2 + 2a + -3a2)' equal to zero and attempt to solve:

Simplifying
-2 + 2a + -3a2 = 0

Solving
-2 + 2a + -3a2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
0.6666666667 + -0.6666666667a + a2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -0.6666666667a + -0.6666666667 + a2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -0.6666666667a + a2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -0.6666666667a + a2 = 0 + -0.6666666667
-0.6666666667a + a2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-0.6666666667a + a2 = -0.6666666667

The a term is -0.6666666667a.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667a + 0.1111111112 + a2 = -0.6666666667 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667a + a2 = -0.6666666667 + 0.1111111112

Combine like terms: -0.6666666667 + 0.1111111112 = -0.5555555555
0.1111111112 + -0.6666666667a + a2 = -0.5555555555

Factor a perfect square on the left side:
(a + -0.3333333334)(a + -0.3333333334) = -0.5555555555

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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