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

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


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

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

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

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

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

Reorder the terms:
2 + 5x + 3x2 = 2x(-4 + 5x)
2 + 5x + 3x2 = (-4 * 2x + 5x * 2x)
2 + 5x + 3x2 = (-8x + 10x2)

Solving
2 + 5x + 3x2 = -8x + 10x2

Solving for variable 'x'.

Reorder the terms:
2 + 5x + 8x + 3x2 + -10x2 = -8x + 10x2 + 8x + -10x2

Combine like terms: 5x + 8x = 13x
2 + 13x + 3x2 + -10x2 = -8x + 10x2 + 8x + -10x2

Combine like terms: 3x2 + -10x2 = -7x2
2 + 13x + -7x2 = -8x + 10x2 + 8x + -10x2

Reorder the terms:
2 + 13x + -7x2 = -8x + 8x + 10x2 + -10x2

Combine like terms: -8x + 8x = 0
2 + 13x + -7x2 = 0 + 10x2 + -10x2
2 + 13x + -7x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
2 + 13x + -7x2 = 0

Factor a trinomial.
(2 + -1x)(1 + 7x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(1 + 7x)' equal to zero and attempt to solve:

Simplifying
1 + 7x = 0

Solving
1 + 7x = 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 + 7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7x = 0 + -1
7x = 0 + -1

Combine like terms: 0 + -1 = -1
7x = -1

Divide each side by '7'.
x = -0.1428571429

Simplifying
x = -0.1428571429
Solution
x = {2, -0.1428571429}

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