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

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


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

Reorder the terms:
(-4 + 5x)(x + -2) = (1 + -5x)(x + 3)

Reorder the terms:
(-4 + 5x)(-2 + x) = (1 + -5x)(x + 3)

Multiply (-4 + 5x) * (-2 + x)
(-4(-2 + x) + 5x * (-2 + x)) = (1 + -5x)(x + 3)
((-2 * -4 + x * -4) + 5x * (-2 + x)) = (1 + -5x)(x + 3)
((8 + -4x) + 5x * (-2 + x)) = (1 + -5x)(x + 3)
(8 + -4x + (-2 * 5x + x * 5x)) = (1 + -5x)(x + 3)
(8 + -4x + (-10x + 5x2)) = (1 + -5x)(x + 3)

Combine like terms: -4x + -10x = -14x
(8 + -14x + 5x2) = (1 + -5x)(x + 3)

Reorder the terms:
8 + -14x + 5x2 = (1 + -5x)(3 + x)

Multiply (1 + -5x) * (3 + x)
8 + -14x + 5x2 = (1(3 + x) + -5x * (3 + x))
8 + -14x + 5x2 = ((3 * 1 + x * 1) + -5x * (3 + x))
8 + -14x + 5x2 = ((3 + 1x) + -5x * (3 + x))
8 + -14x + 5x2 = (3 + 1x + (3 * -5x + x * -5x))
8 + -14x + 5x2 = (3 + 1x + (-15x + -5x2))

Combine like terms: 1x + -15x = -14x
8 + -14x + 5x2 = (3 + -14x + -5x2)

Add '14x' to each side of the equation.
8 + -14x + 14x + 5x2 = 3 + -14x + 14x + -5x2

Combine like terms: -14x + 14x = 0
8 + 0 + 5x2 = 3 + -14x + 14x + -5x2
8 + 5x2 = 3 + -14x + 14x + -5x2

Combine like terms: -14x + 14x = 0
8 + 5x2 = 3 + 0 + -5x2
8 + 5x2 = 3 + -5x2

Solving
8 + 5x2 = 3 + -5x2

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '5x2' to each side of the equation.
8 + 5x2 + 5x2 = 3 + -5x2 + 5x2

Combine like terms: 5x2 + 5x2 = 10x2
8 + 10x2 = 3 + -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
8 + 10x2 = 3 + 0
8 + 10x2 = 3

Add '-8' to each side of the equation.
8 + -8 + 10x2 = 3 + -8

Combine like terms: 8 + -8 = 0
0 + 10x2 = 3 + -8
10x2 = 3 + -8

Combine like terms: 3 + -8 = -5
10x2 = -5

Divide each side by '10'.
x2 = -0.5

Simplifying
x2 = -0.5

Reorder the terms:
0.5 + x2 = -0.5 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.5 + x2 = 0.0

The solution to this equation could not be determined.

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