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

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


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

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

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

Multiply (1 + 5x) * (-3 + 2x)
(1(-3 + 2x) + 5x * (-3 + 2x)) = 4x(x + -5)
((-3 * 1 + 2x * 1) + 5x * (-3 + 2x)) = 4x(x + -5)
((-3 + 2x) + 5x * (-3 + 2x)) = 4x(x + -5)
(-3 + 2x + (-3 * 5x + 2x * 5x)) = 4x(x + -5)
(-3 + 2x + (-15x + 10x2)) = 4x(x + -5)

Combine like terms: 2x + -15x = -13x
(-3 + -13x + 10x2) = 4x(x + -5)

Reorder the terms:
-3 + -13x + 10x2 = 4x(-5 + x)
-3 + -13x + 10x2 = (-5 * 4x + x * 4x)
-3 + -13x + 10x2 = (-20x + 4x2)

Solving
-3 + -13x + 10x2 = -20x + 4x2

Solving for variable 'x'.

Reorder the terms:
-3 + -13x + 20x + 10x2 + -4x2 = -20x + 4x2 + 20x + -4x2

Combine like terms: -13x + 20x = 7x
-3 + 7x + 10x2 + -4x2 = -20x + 4x2 + 20x + -4x2

Combine like terms: 10x2 + -4x2 = 6x2
-3 + 7x + 6x2 = -20x + 4x2 + 20x + -4x2

Reorder the terms:
-3 + 7x + 6x2 = -20x + 20x + 4x2 + -4x2

Combine like terms: -20x + 20x = 0
-3 + 7x + 6x2 = 0 + 4x2 + -4x2
-3 + 7x + 6x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-3 + 7x + 6x2 = 0

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


Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-1.5, 0.3333333333}

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