2(2-8x)5x=6(3+5x)

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Solution for 2(2-8x)5x=6(3+5x) equation:


Simplifying
2(2 + -8x) * 5x = 6(3 + 5x)

Reorder the terms for easier multiplication:
2 * 5x(2 + -8x) = 6(3 + 5x)

Multiply 2 * 5
10x(2 + -8x) = 6(3 + 5x)
(2 * 10x + -8x * 10x) = 6(3 + 5x)
(20x + -80x2) = 6(3 + 5x)
20x + -80x2 = (3 * 6 + 5x * 6)
20x + -80x2 = (18 + 30x)

Solving
20x + -80x2 = 18 + 30x

Solving for variable 'x'.

Reorder the terms:
-18 + 20x + -30x + -80x2 = 18 + 30x + -18 + -30x

Combine like terms: 20x + -30x = -10x
-18 + -10x + -80x2 = 18 + 30x + -18 + -30x

Reorder the terms:
-18 + -10x + -80x2 = 18 + -18 + 30x + -30x

Combine like terms: 18 + -18 = 0
-18 + -10x + -80x2 = 0 + 30x + -30x
-18 + -10x + -80x2 = 30x + -30x

Combine like terms: 30x + -30x = 0
-18 + -10x + -80x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(9 + 5x + 40x2) = 0

Ignore the factor -2.

Subproblem 1

Set the factor '(9 + 5x + 40x2)' equal to zero and attempt to solve: Simplifying 9 + 5x + 40x2 = 0 Solving 9 + 5x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. 0.225 + 0.125x + x2 = 0.0 Move the constant term to the right: Add '-0.225' to each side of the equation. 0.225 + 0.125x + -0.225 + x2 = 0.0 + -0.225 Reorder the terms: 0.225 + -0.225 + 0.125x + x2 = 0.0 + -0.225 Combine like terms: 0.225 + -0.225 = 0.000 0.000 + 0.125x + x2 = 0.0 + -0.225 0.125x + x2 = 0.0 + -0.225 Combine like terms: 0.0 + -0.225 = -0.225 0.125x + x2 = -0.225 The x term is 0.125x. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125x + 0.00390625 + x2 = -0.225 + 0.00390625 Reorder the terms: 0.00390625 + 0.125x + x2 = -0.225 + 0.00390625 Combine like terms: -0.225 + 0.00390625 = -0.22109375 0.00390625 + 0.125x + x2 = -0.22109375 Factor a perfect square on the left side: (x + 0.0625)(x + 0.0625) = -0.22109375 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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