(5x+2)(10x-3)=(2x+3)(x-8)

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Solution for (5x+2)(10x-3)=(2x+3)(x-8) equation:


Simplifying
(5x + 2)(10x + -3) = (2x + 3)(x + -8)

Reorder the terms:
(2 + 5x)(10x + -3) = (2x + 3)(x + -8)

Reorder the terms:
(2 + 5x)(-3 + 10x) = (2x + 3)(x + -8)

Multiply (2 + 5x) * (-3 + 10x)
(2(-3 + 10x) + 5x * (-3 + 10x)) = (2x + 3)(x + -8)
((-3 * 2 + 10x * 2) + 5x * (-3 + 10x)) = (2x + 3)(x + -8)
((-6 + 20x) + 5x * (-3 + 10x)) = (2x + 3)(x + -8)
(-6 + 20x + (-3 * 5x + 10x * 5x)) = (2x + 3)(x + -8)
(-6 + 20x + (-15x + 50x2)) = (2x + 3)(x + -8)

Combine like terms: 20x + -15x = 5x
(-6 + 5x + 50x2) = (2x + 3)(x + -8)

Reorder the terms:
-6 + 5x + 50x2 = (3 + 2x)(x + -8)

Reorder the terms:
-6 + 5x + 50x2 = (3 + 2x)(-8 + x)

Multiply (3 + 2x) * (-8 + x)
-6 + 5x + 50x2 = (3(-8 + x) + 2x * (-8 + x))
-6 + 5x + 50x2 = ((-8 * 3 + x * 3) + 2x * (-8 + x))
-6 + 5x + 50x2 = ((-24 + 3x) + 2x * (-8 + x))
-6 + 5x + 50x2 = (-24 + 3x + (-8 * 2x + x * 2x))
-6 + 5x + 50x2 = (-24 + 3x + (-16x + 2x2))

Combine like terms: 3x + -16x = -13x
-6 + 5x + 50x2 = (-24 + -13x + 2x2)

Solving
-6 + 5x + 50x2 = -24 + -13x + 2x2

Solving for variable 'x'.

Reorder the terms:
-6 + 24 + 5x + 13x + 50x2 + -2x2 = -24 + -13x + 2x2 + 24 + 13x + -2x2

Combine like terms: -6 + 24 = 18
18 + 5x + 13x + 50x2 + -2x2 = -24 + -13x + 2x2 + 24 + 13x + -2x2

Combine like terms: 5x + 13x = 18x
18 + 18x + 50x2 + -2x2 = -24 + -13x + 2x2 + 24 + 13x + -2x2

Combine like terms: 50x2 + -2x2 = 48x2
18 + 18x + 48x2 = -24 + -13x + 2x2 + 24 + 13x + -2x2

Reorder the terms:
18 + 18x + 48x2 = -24 + 24 + -13x + 13x + 2x2 + -2x2

Combine like terms: -24 + 24 = 0
18 + 18x + 48x2 = 0 + -13x + 13x + 2x2 + -2x2
18 + 18x + 48x2 = -13x + 13x + 2x2 + -2x2

Combine like terms: -13x + 13x = 0
18 + 18x + 48x2 = 0 + 2x2 + -2x2
18 + 18x + 48x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
18 + 18x + 48x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + 3x + 8x2) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(3 + 3x + 8x2)' equal to zero and attempt to solve: Simplifying 3 + 3x + 8x2 = 0 Solving 3 + 3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + 0.375x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 0.375x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 0.375x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 0.375x + x2 = 0 + -0.375 0.375x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 0.375x + x2 = -0.375 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = -0.375 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = -0.375 + 0.03515625 Combine like terms: -0.375 + 0.03515625 = -0.33984375 0.03515625 + 0.375x + x2 = -0.33984375 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = -0.33984375 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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