2x(3-4x)=10

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Solution for 2x(3-4x)=10 equation:


Simplifying
2x(3 + -4x) = 10
(3 * 2x + -4x * 2x) = 10
(6x + -8x2) = 10

Solving
6x + -8x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 6x + -8x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 6x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 3x + -4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 3x + -4x2)' equal to zero and attempt to solve:

Simplifying
-5 + 3x + -4x2 = 0

Solving
-5 + 3x + -4x2 = 0

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

Divide each side by '-4'.
1.25 + -0.75x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -0.75x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -0.75x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -0.75x + x2 = 0 + -1.25
-0.75x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-0.75x + x2 = -1.25

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = -1.25 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = -1.25 + 0.140625

Combine like terms: -1.25 + 0.140625 = -1.109375
0.140625 + -0.75x + x2 = -1.109375

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = -1.109375

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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