7x^2-12x=19

Solution for 7x^2-12x=19 equation:

Simplifying
7x2 + -12x = 19

Reorder the terms:
-12x + 7x2 = 19

Solving
-12x + 7x2 = 19

Solving for variable 'x'.

Reorder the terms:
-19 + -12x + 7x2 = 19 + -19

Combine like terms: 19 + -19 = 0
-19 + -12x + 7x2 = 0

Factor a trinomial.
(-1 + -1x)(19 + -7x) = 0

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 '(19 + -7x)' equal to zero and attempt to solve:

Simplifying
19 + -7x = 0

Solving
19 + -7x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -7x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -7x = 0 + -19
-7x = 0 + -19

Combine like terms: 0 + -19 = -19
-7x = -19

Divide each side by '-7'.
x = 2.714285714

Simplifying
x = 2.714285714
Solution
x = {-1, 2.714285714}