2x^2-11x+3=5x+3

Solution for 2x^2-11x+3=5x+3 equation:

Simplifying
2x2 + -11x + 3 = 5x + 3

Reorder the terms:
3 + -11x + 2x2 = 5x + 3

Reorder the terms:
3 + -11x + 2x2 = 3 + 5x

Add '-3' to each side of the equation.
3 + -11x + -3 + 2x2 = 3 + -3 + 5x

Reorder the terms:
3 + -3 + -11x + 2x2 = 3 + -3 + 5x

Combine like terms: 3 + -3 = 0
0 + -11x + 2x2 = 3 + -3 + 5x
-11x + 2x2 = 3 + -3 + 5x

Combine like terms: 3 + -3 = 0
-11x + 2x2 = 0 + 5x
-11x + 2x2 = 5x

Solving
-11x + 2x2 = 5x

Solving for variable 'x'.

Reorder the terms:
-11x + -5x + 2x2 = 5x + -5x

Combine like terms: -11x + -5x = -16x
-16x + 2x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-8 + x) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8
Solution
x = {0, 8}