2x(x-4)=-13x+3

Solution for 2x(x-4)=-13x+3 equation:

Simplifying
2x(x + -4) = -13x + 3

Reorder the terms:
2x(-4 + x) = -13x + 3
(-4 * 2x + x * 2x) = -13x + 3
(-8x + 2x2) = -13x + 3

Reorder the terms:
-8x + 2x2 = 3 + -13x

Solving
-8x + 2x2 = 3 + -13x

Solving for variable 'x'.

Reorder the terms:
-3 + -8x + 13x + 2x2 = 3 + -13x + -3 + 13x

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

Reorder the terms:
-3 + 5x + 2x2 = 3 + -3 + -13x + 13x

Combine like terms: 3 + -3 = 0
-3 + 5x + 2x2 = 0 + -13x + 13x
-3 + 5x + 2x2 = -13x + 13x

Combine like terms: -13x + 13x = 0
-3 + 5x + 2x2 = 0

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

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3
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 = {-3, 0.5}