(3x^2)+(4x)-(12)=(24)-(19x)

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Solution for (3x^2)+(4x)-(12)=(24)-(19x) equation: 


Simplifying
(3x2) + (4x) + -1(12) = (24) + -1(19x)

Multiply -1 * 12
(3x2) + (4x) + -12 = (24) + -1(19x)

Reorder the terms:
-12 + (4x) + (3x2) = (24) + -1(19x)
-12 + (4x) + (3x2) = 24 + -1(19x)

Remove parenthesis around (19x)
-12 + (4x) + (3x2) = 24 + -1 * 19x

Multiply -1 * 19
-12 + (4x) + (3x2) = 24 + -19x

Solving
-12 + (4x) + (3x2) = 24 + -19x

Solving for variable 'x'.

Reorder the terms:
-12 + -24 + (4x) + 19x + (3x2) = 24 + -19x + -24 + 19x

Combine like terms: -12 + -24 = -36
-36 + (4x) + 19x + (3x2) = 24 + -19x + -24 + 19x

Combine like terms: (4x) + 19x = 23x
-36 + 23x + (3x2) = 24 + -19x + -24 + 19x

Reorder the terms:
-36 + 23x + (3x2) = 24 + -24 + -19x + 19x

Combine like terms: 24 + -24 = 0
-36 + 23x + (3x2) = 0 + -19x + 19x
-36 + 23x + (3x2) = -19x + 19x

Combine like terms: -19x + 19x = 0
-36 + 23x + (3x2) = 0

Factor a trinomial.
(-9 + -1x)(4 + -3x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
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
Solution
x = {-9, 1.333333333}

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