2x^2-7x=11x+20

Solution for 2x^2-7x=11x+20 equation:

Simplifying
2x2 + -7x = 11x + 20

Reorder the terms:
-7x + 2x2 = 11x + 20

Reorder the terms:
-7x + 2x2 = 20 + 11x

Solving
-7x + 2x2 = 20 + 11x

Solving for variable 'x'.

Reorder the terms:
-20 + -7x + -11x + 2x2 = 20 + 11x + -20 + -11x

Combine like terms: -7x + -11x = -18x
-20 + -18x + 2x2 = 20 + 11x + -20 + -11x

Reorder the terms:
-20 + -18x + 2x2 = 20 + -20 + 11x + -11x

Combine like terms: 20 + -20 = 0
-20 + -18x + 2x2 = 0 + 11x + -11x
-20 + -18x + 2x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
-20 + -18x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -9x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(10 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-1, 10}