40x^2-23x=6+5x^2

Solution for 40x^2-23x=6+5x^2 equation:

Simplifying
40x2 + -23x = 6 + 5x2

Reorder the terms:
-23x + 40x2 = 6 + 5x2

Solving
-23x + 40x2 = 6 + 5x2

Solving for variable 'x'.

Reorder the terms:
-6 + -23x + 40x2 + -5x2 = 6 + 5x2 + -6 + -5x2

Combine like terms: 40x2 + -5x2 = 35x2
-6 + -23x + 35x2 = 6 + 5x2 + -6 + -5x2

Reorder the terms:
-6 + -23x + 35x2 = 6 + -6 + 5x2 + -5x2

Combine like terms: 6 + -6 = 0
-6 + -23x + 35x2 = 0 + 5x2 + -5x2
-6 + -23x + 35x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-6 + -23x + 35x2 = 0

Factor a trinomial.
(-1 + -5x)(6 + -7x) = 0

Subproblem 1
Set the factor '(-1 + -5x)' equal to zero and attempt to solve:

Simplifying
-1 + -5x = 0

Solving
-1 + -5x = 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 + -5x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5x = 0 + 1
-5x = 0 + 1

Combine like terms: 0 + 1 = 1
-5x = 1

Divide each side by '-5'.
x = -0.2

Simplifying
x = -0.2
Subproblem 2
Set the factor '(6 + -7x)' equal to zero and attempt to solve:

Simplifying
6 + -7x = 0

Solving
6 + -7x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7x = 0 + -6
-7x = 0 + -6

Combine like terms: 0 + -6 = -6
-7x = -6

Divide each side by '-7'.
x = 0.8571428571

Simplifying
x = 0.8571428571
Solution
x = {-0.2, 0.8571428571}