13x^2-28x+13=-3+3x^2

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Solution for 13x^2-28x+13=-3+3x^2 equation: 


Simplifying
13x2 + -28x + 13 = -3 + 3x2

Reorder the terms:
13 + -28x + 13x2 = -3 + 3x2

Solving
13 + -28x + 13x2 = -3 + 3x2

Solving for variable 'x'.

Reorder the terms:
13 + 3 + -28x + 13x2 + -3x2 = -3 + 3x2 + 3 + -3x2

Combine like terms: 13 + 3 = 16
16 + -28x + 13x2 + -3x2 = -3 + 3x2 + 3 + -3x2

Combine like terms: 13x2 + -3x2 = 10x2
16 + -28x + 10x2 = -3 + 3x2 + 3 + -3x2

Reorder the terms:
16 + -28x + 10x2 = -3 + 3 + 3x2 + -3x2

Combine like terms: -3 + 3 = 0
16 + -28x + 10x2 = 0 + 3x2 + -3x2
16 + -28x + 10x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
16 + -28x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -14x + 5x2) = 0

Factor a trinomial.
2((4 + -5x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 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 + -5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x = 0 + -4
-5x = 0 + -4

Combine like terms: 0 + -4 = -4
-5x = -4

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8

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 = {0.8, 2}

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