40x^2-3x-7=-6

Solution for 40x^2-3x-7=-6 equation:

Simplifying
40x2 + -3x + -7 = -6

Reorder the terms:
-7 + -3x + 40x2 = -6

Solving
-7 + -3x + 40x2 = -6

Solving for variable 'x'.

Reorder the terms:
-7 + 6 + -3x + 40x2 = -6 + 6

Combine like terms: -7 + 6 = -1
-1 + -3x + 40x2 = -6 + 6

Combine like terms: -6 + 6 = 0
-1 + -3x + 40x2 = 0

Factor a trinomial.
(-1 + -8x)(1 + -5x) = 0

Subproblem 1
Set the factor '(-1 + -8x)' equal to zero and attempt to solve:

Simplifying
-1 + -8x = 0

Solving
-1 + -8x = 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 + -8x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8x = 0 + 1
-8x = 0 + 1

Combine like terms: 0 + 1 = 1
-8x = 1

Divide each side by '-8'.
x = -0.125

Simplifying
x = -0.125
Subproblem 2
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
Solution
x = {-0.125, 0.2}