4x^2+5x+12=-2x^2+23

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Solution for 4x^2+5x+12=-2x^2+23 equation: 


Simplifying
4x2 + 5x + 12 = -2x2 + 23

Reorder the terms:
12 + 5x + 4x2 = -2x2 + 23

Reorder the terms:
12 + 5x + 4x2 = 23 + -2x2

Solving
12 + 5x + 4x2 = 23 + -2x2

Solving for variable 'x'.

Reorder the terms:
12 + -23 + 5x + 4x2 + 2x2 = 23 + -2x2 + -23 + 2x2

Combine like terms: 12 + -23 = -11
-11 + 5x + 4x2 + 2x2 = 23 + -2x2 + -23 + 2x2

Combine like terms: 4x2 + 2x2 = 6x2
-11 + 5x + 6x2 = 23 + -2x2 + -23 + 2x2

Reorder the terms:
-11 + 5x + 6x2 = 23 + -23 + -2x2 + 2x2

Combine like terms: 23 + -23 = 0
-11 + 5x + 6x2 = 0 + -2x2 + 2x2
-11 + 5x + 6x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-11 + 5x + 6x2 = 0

Factor a trinomial.
(-11 + -6x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-11 + -6x)' equal to zero and attempt to solve:

Simplifying
-11 + -6x = 0

Solving
-11 + -6x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -6x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -6x = 0 + 11
-6x = 0 + 11

Combine like terms: 0 + 11 = 11
-6x = 11

Divide each side by '-6'.
x = -1.833333333

Simplifying
x = -1.833333333

Subproblem 2
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
Solution
x = {-1.833333333, 1}

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