4x(5x+1)=8x+2(x-3)

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Solution for 4x(5x+1)=8x+2(x-3) equation:


Simplifying
4x(5x + 1) = 8x + 2(x + -3)

Reorder the terms:
4x(1 + 5x) = 8x + 2(x + -3)
(1 * 4x + 5x * 4x) = 8x + 2(x + -3)
(4x + 20x2) = 8x + 2(x + -3)

Reorder the terms:
4x + 20x2 = 8x + 2(-3 + x)
4x + 20x2 = 8x + (-3 * 2 + x * 2)
4x + 20x2 = 8x + (-6 + 2x)

Reorder the terms:
4x + 20x2 = -6 + 8x + 2x

Combine like terms: 8x + 2x = 10x
4x + 20x2 = -6 + 10x

Solving
4x + 20x2 = -6 + 10x

Solving for variable 'x'.

Reorder the terms:
6 + 4x + -10x + 20x2 = -6 + 10x + 6 + -10x

Combine like terms: 4x + -10x = -6x
6 + -6x + 20x2 = -6 + 10x + 6 + -10x

Reorder the terms:
6 + -6x + 20x2 = -6 + 6 + 10x + -10x

Combine like terms: -6 + 6 = 0
6 + -6x + 20x2 = 0 + 10x + -10x
6 + -6x + 20x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
6 + -6x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -3x + 10x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + -3x + 10x2)' equal to zero and attempt to solve: Simplifying 3 + -3x + 10x2 = 0 Solving 3 + -3x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.3 + -0.3x + x2 = 0.0 Move the constant term to the right: Add '-0.3' to each side of the equation. 0.3 + -0.3x + -0.3 + x2 = 0.0 + -0.3 Reorder the terms: 0.3 + -0.3 + -0.3x + x2 = 0.0 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + -0.3x + x2 = 0.0 + -0.3 -0.3x + x2 = 0.0 + -0.3 Combine like terms: 0.0 + -0.3 = -0.3 -0.3x + x2 = -0.3 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = -0.3 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = -0.3 + 0.0225 Combine like terms: -0.3 + 0.0225 = -0.2775 0.0225 + -0.3x + x2 = -0.2775 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = -0.2775 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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