2x^2=7x-6

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

Simplifying
2x2 = 7x + -6

Reorder the terms:
2x2 = -6 + 7x

Solving
2x2 = -6 + 7x

Solving for variable 'x'.

Reorder the terms:
6 + -7x + 2x2 = -6 + 7x + 6 + -7x

Reorder the terms:
6 + -7x + 2x2 = -6 + 6 + 7x + -7x

Combine like terms: -6 + 6 = 0
6 + -7x + 2x2 = 0 + 7x + -7x
6 + -7x + 2x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
6 + -7x + 2x2 = 0

Factor a trinomial.
(3 + -2x)(2 + -1x) = 0

Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1.5, 2}