4x^2-13x+3=-8x+2

Solution for 4x^2-13x+3=-8x+2 equation:

Simplifying
4x2 + -13x + 3 = -8x + 2

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

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

Solving
3 + -13x + 4x2 = 2 + -8x

Solving for variable 'x'.

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

Combine like terms: 3 + -2 = 1
1 + -13x + 8x + 4x2 = 2 + -8x + -2 + 8x

Combine like terms: -13x + 8x = -5x
1 + -5x + 4x2 = 2 + -8x + -2 + 8x

Reorder the terms:
1 + -5x + 4x2 = 2 + -2 + -8x + 8x

Combine like terms: 2 + -2 = 0
1 + -5x + 4x2 = 0 + -8x + 8x
1 + -5x + 4x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
1 + -5x + 4x2 = 0

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

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

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {0.25, 1}