3x^2-23x=-4x^2-3x-12

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Solution for 3x^2-23x=-4x^2-3x-12 equation: 


Simplifying
3x2 + -23x = -4x2 + -3x + -12

Reorder the terms:
-23x + 3x2 = -4x2 + -3x + -12

Reorder the terms:
-23x + 3x2 = -12 + -3x + -4x2

Solving
-23x + 3x2 = -12 + -3x + -4x2

Solving for variable 'x'.

Reorder the terms:
12 + -23x + 3x + 3x2 + 4x2 = -12 + -3x + -4x2 + 12 + 3x + 4x2

Combine like terms: -23x + 3x = -20x
12 + -20x + 3x2 + 4x2 = -12 + -3x + -4x2 + 12 + 3x + 4x2

Combine like terms: 3x2 + 4x2 = 7x2
12 + -20x + 7x2 = -12 + -3x + -4x2 + 12 + 3x + 4x2

Reorder the terms:
12 + -20x + 7x2 = -12 + 12 + -3x + 3x + -4x2 + 4x2

Combine like terms: -12 + 12 = 0
12 + -20x + 7x2 = 0 + -3x + 3x + -4x2 + 4x2
12 + -20x + 7x2 = -3x + 3x + -4x2 + 4x2

Combine like terms: -3x + 3x = 0
12 + -20x + 7x2 = 0 + -4x2 + 4x2
12 + -20x + 7x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
12 + -20x + 7x2 = 0

Factor a trinomial.
(6 + -7x)(2 + -1x) = 0


Subproblem 1
Set the factor '(6 + -7x)' equal to zero and attempt to solve:

Simplifying
6 + -7x = 0

Solving
6 + -7x = 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 + -7x = 0 + -6

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

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

Divide each side by '-7'.
x = 0.8571428571

Simplifying
x = 0.8571428571

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 = {0.8571428571, 2}

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