10x^2-7x=6

Solution for 10x^2-7x=6 equation:

Simplifying
10x2 + -7x = 6

Reorder the terms:
-7x + 10x2 = 6

Solving
-7x + 10x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + -7x + 10x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -7x + 10x2 = 0

Factor a trinomial.
(-1 + -2x)(6 + -5x) = 0

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
Set the factor '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 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 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2
Solution
x = {-0.5, 1.2}