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

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

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

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

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

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

Combine like terms: 3x + -2x = 1x
(-3 + 1x + 2x2) = 2(5x + 1)

Reorder the terms:
-3 + 1x + 2x2 = 2(1 + 5x)
-3 + 1x + 2x2 = (1 * 2 + 5x * 2)
-3 + 1x + 2x2 = (2 + 10x)

Solving
-3 + 1x + 2x2 = 2 + 10x

Solving for variable 'x'.

Reorder the terms:
-3 + -2 + 1x + -10x + 2x2 = 2 + 10x + -2 + -10x

Combine like terms: -3 + -2 = -5
-5 + 1x + -10x + 2x2 = 2 + 10x + -2 + -10x

Combine like terms: 1x + -10x = -9x
-5 + -9x + 2x2 = 2 + 10x + -2 + -10x

Reorder the terms:
-5 + -9x + 2x2 = 2 + -2 + 10x + -10x

Combine like terms: 2 + -2 = 0
-5 + -9x + 2x2 = 0 + 10x + -10x
-5 + -9x + 2x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-5 + -9x + 2x2 = 0

Factor a trinomial.
(-1 + -2x)(5 + -1x) = 0

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-0.5, 5}