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

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


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

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

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

Multiply (-2 + x) * (1 + 3x)
5(-2(1 + 3x) + x(1 + 3x)) = 4(x + -2)(2 + -5x)
5((1 * -2 + 3x * -2) + x(1 + 3x)) = 4(x + -2)(2 + -5x)
5((-2 + -6x) + x(1 + 3x)) = 4(x + -2)(2 + -5x)
5(-2 + -6x + (1 * x + 3x * x)) = 4(x + -2)(2 + -5x)
5(-2 + -6x + (1x + 3x2)) = 4(x + -2)(2 + -5x)

Combine like terms: -6x + 1x = -5x
5(-2 + -5x + 3x2) = 4(x + -2)(2 + -5x)
(-2 * 5 + -5x * 5 + 3x2 * 5) = 4(x + -2)(2 + -5x)
(-10 + -25x + 15x2) = 4(x + -2)(2 + -5x)

Reorder the terms:
-10 + -25x + 15x2 = 4(-2 + x)(2 + -5x)

Multiply (-2 + x) * (2 + -5x)
-10 + -25x + 15x2 = 4(-2(2 + -5x) + x(2 + -5x))
-10 + -25x + 15x2 = 4((2 * -2 + -5x * -2) + x(2 + -5x))
-10 + -25x + 15x2 = 4((-4 + 10x) + x(2 + -5x))
-10 + -25x + 15x2 = 4(-4 + 10x + (2 * x + -5x * x))
-10 + -25x + 15x2 = 4(-4 + 10x + (2x + -5x2))

Combine like terms: 10x + 2x = 12x
-10 + -25x + 15x2 = 4(-4 + 12x + -5x2)
-10 + -25x + 15x2 = (-4 * 4 + 12x * 4 + -5x2 * 4)
-10 + -25x + 15x2 = (-16 + 48x + -20x2)

Solving
-10 + -25x + 15x2 = -16 + 48x + -20x2

Solving for variable 'x'.

Reorder the terms:
-10 + 16 + -25x + -48x + 15x2 + 20x2 = -16 + 48x + -20x2 + 16 + -48x + 20x2

Combine like terms: -10 + 16 = 6
6 + -25x + -48x + 15x2 + 20x2 = -16 + 48x + -20x2 + 16 + -48x + 20x2

Combine like terms: -25x + -48x = -73x
6 + -73x + 15x2 + 20x2 = -16 + 48x + -20x2 + 16 + -48x + 20x2

Combine like terms: 15x2 + 20x2 = 35x2
6 + -73x + 35x2 = -16 + 48x + -20x2 + 16 + -48x + 20x2

Reorder the terms:
6 + -73x + 35x2 = -16 + 16 + 48x + -48x + -20x2 + 20x2

Combine like terms: -16 + 16 = 0
6 + -73x + 35x2 = 0 + 48x + -48x + -20x2 + 20x2
6 + -73x + 35x2 = 48x + -48x + -20x2 + 20x2

Combine like terms: 48x + -48x = 0
6 + -73x + 35x2 = 0 + -20x2 + 20x2
6 + -73x + 35x2 = -20x2 + 20x2

Combine like terms: -20x2 + 20x2 = 0
6 + -73x + 35x2 = 0

Factor a trinomial.
(3 + -35x)(2 + -1x) = 0


Subproblem 1
Set the factor '(3 + -35x)' equal to zero and attempt to solve:

Simplifying
3 + -35x = 0

Solving
3 + -35x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -35x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -35x = 0 + -3
-35x = 0 + -3

Combine like terms: 0 + -3 = -3
-35x = -3

Divide each side by '-35'.
x = 0.08571428571

Simplifying
x = 0.08571428571

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.08571428571, 2}

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