11x^2-2x+13=7x^2-15x+3

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Solution for 11x^2-2x+13=7x^2-15x+3 equation: 


Simplifying
11x2 + -2x + 13 = 7x2 + -15x + 3

Reorder the terms:
13 + -2x + 11x2 = 7x2 + -15x + 3

Reorder the terms:
13 + -2x + 11x2 = 3 + -15x + 7x2

Solving
13 + -2x + 11x2 = 3 + -15x + 7x2

Solving for variable 'x'.

Reorder the terms:
13 + -3 + -2x + 15x + 11x2 + -7x2 = 3 + -15x + 7x2 + -3 + 15x + -7x2

Combine like terms: 13 + -3 = 10
10 + -2x + 15x + 11x2 + -7x2 = 3 + -15x + 7x2 + -3 + 15x + -7x2

Combine like terms: -2x + 15x = 13x
10 + 13x + 11x2 + -7x2 = 3 + -15x + 7x2 + -3 + 15x + -7x2

Combine like terms: 11x2 + -7x2 = 4x2
10 + 13x + 4x2 = 3 + -15x + 7x2 + -3 + 15x + -7x2

Reorder the terms:
10 + 13x + 4x2 = 3 + -3 + -15x + 15x + 7x2 + -7x2

Combine like terms: 3 + -3 = 0
10 + 13x + 4x2 = 0 + -15x + 15x + 7x2 + -7x2
10 + 13x + 4x2 = -15x + 15x + 7x2 + -7x2

Combine like terms: -15x + 15x = 0
10 + 13x + 4x2 = 0 + 7x2 + -7x2
10 + 13x + 4x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
10 + 13x + 4x2 = 0

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


Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(5 + 4x)' equal to zero and attempt to solve:

Simplifying
5 + 4x = 0

Solving
5 + 4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4x = 0 + -5

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

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

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25
Solution
x = {-2, -1.25}

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