2x^2-21x=-3x^2-5x-12

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Solution for 2x^2-21x=-3x^2-5x-12 equation: 


Simplifying
2x2 + -21x = -3x2 + -5x + -12

Reorder the terms:
-21x + 2x2 = -3x2 + -5x + -12

Reorder the terms:
-21x + 2x2 = -12 + -5x + -3x2

Solving
-21x + 2x2 = -12 + -5x + -3x2

Solving for variable 'x'.

Reorder the terms:
12 + -21x + 5x + 2x2 + 3x2 = -12 + -5x + -3x2 + 12 + 5x + 3x2

Combine like terms: -21x + 5x = -16x
12 + -16x + 2x2 + 3x2 = -12 + -5x + -3x2 + 12 + 5x + 3x2

Combine like terms: 2x2 + 3x2 = 5x2
12 + -16x + 5x2 = -12 + -5x + -3x2 + 12 + 5x + 3x2

Reorder the terms:
12 + -16x + 5x2 = -12 + 12 + -5x + 5x + -3x2 + 3x2

Combine like terms: -12 + 12 = 0
12 + -16x + 5x2 = 0 + -5x + 5x + -3x2 + 3x2
12 + -16x + 5x2 = -5x + 5x + -3x2 + 3x2

Combine like terms: -5x + 5x = 0
12 + -16x + 5x2 = 0 + -3x2 + 3x2
12 + -16x + 5x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
12 + -16x + 5x2 = 0

Factor a trinomial.
(6 + -5x)(2 + -1x) = 0


Subproblem 1
Set the factor '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 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 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2

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 = {1.2, 2}

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