6x^2-12-4x=19x-32

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Solution for 6x^2-12-4x=19x-32 equation: 


Simplifying
6x2 + -12 + -4x = 19x + -32

Reorder the terms:
-12 + -4x + 6x2 = 19x + -32

Reorder the terms:
-12 + -4x + 6x2 = -32 + 19x

Solving
-12 + -4x + 6x2 = -32 + 19x

Solving for variable 'x'.

Reorder the terms:
-12 + 32 + -4x + -19x + 6x2 = -32 + 19x + 32 + -19x

Combine like terms: -12 + 32 = 20
20 + -4x + -19x + 6x2 = -32 + 19x + 32 + -19x

Combine like terms: -4x + -19x = -23x
20 + -23x + 6x2 = -32 + 19x + 32 + -19x

Reorder the terms:
20 + -23x + 6x2 = -32 + 32 + 19x + -19x

Combine like terms: -32 + 32 = 0
20 + -23x + 6x2 = 0 + 19x + -19x
20 + -23x + 6x2 = 19x + -19x

Combine like terms: 19x + -19x = 0
20 + -23x + 6x2 = 0

Factor a trinomial.
(4 + -3x)(5 + -2x) = 0


Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {1.333333333, 2.5}

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