3(x-1)=x(8x+13)

Solution for 3(x-1)=x(8x+13) equation:

Simplifying
3(x + -1) = x(8x + 13)

Reorder the terms:
3(-1 + x) = x(8x + 13)
(-1 * 3 + x * 3) = x(8x + 13)
(-3 + 3x) = x(8x + 13)

Reorder the terms:
-3 + 3x = x(13 + 8x)
-3 + 3x = (13 * x + 8x * x)
-3 + 3x = (13x + 8x2)

Solving
-3 + 3x = 13x + 8x2

Solving for variable 'x'.

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

Reorder the terms:
-3 + -10x + -8x2 = 13x + -13x + 8x2 + -8x2

Combine like terms: 13x + -13x = 0
-3 + -10x + -8x2 = 0 + 8x2 + -8x2
-3 + -10x + -8x2 = 8x2 + -8x2

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 10x + 8x2) = 0

Factor a trinomial.
-1((3 + 4x)(1 + 2x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 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 + 4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4x = 0 + -3
4x = 0 + -3

Combine like terms: 0 + -3 = -3
4x = -3

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75
Subproblem 2
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
Solution
x = {-0.75, -0.5}