2(x+13)=7x+2(x^2-13)

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Solution for 2(x+13)=7x+2(x^2-13) equation: 


Simplifying
2(x + 13) = 7x + 2(x2 + -13)

Reorder the terms:
2(13 + x) = 7x + 2(x2 + -13)
(13 * 2 + x * 2) = 7x + 2(x2 + -13)
(26 + 2x) = 7x + 2(x2 + -13)

Reorder the terms:
26 + 2x = 7x + 2(-13 + x2)
26 + 2x = 7x + (-13 * 2 + x2 * 2)
26 + 2x = 7x + (-26 + 2x2)

Reorder the terms:
26 + 2x = -26 + 7x + 2x2

Solving
26 + 2x = -26 + 7x + 2x2

Solving for variable 'x'.

Reorder the terms:
26 + 26 + 2x + -7x + -2x2 = -26 + 7x + 2x2 + 26 + -7x + -2x2

Combine like terms: 26 + 26 = 52
52 + 2x + -7x + -2x2 = -26 + 7x + 2x2 + 26 + -7x + -2x2

Combine like terms: 2x + -7x = -5x
52 + -5x + -2x2 = -26 + 7x + 2x2 + 26 + -7x + -2x2

Reorder the terms:
52 + -5x + -2x2 = -26 + 26 + 7x + -7x + 2x2 + -2x2

Combine like terms: -26 + 26 = 0
52 + -5x + -2x2 = 0 + 7x + -7x + 2x2 + -2x2
52 + -5x + -2x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
52 + -5x + -2x2 = 0 + 2x2 + -2x2
52 + -5x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
52 + -5x + -2x2 = 0

Factor a trinomial.
(4 + -1x)(13 + 2x) = 0


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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(13 + 2x)' equal to zero and attempt to solve:

Simplifying
13 + 2x = 0

Solving
13 + 2x = 0

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

Add '-13' to each side of the equation.
13 + -13 + 2x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 2x = 0 + -13
2x = 0 + -13

Combine like terms: 0 + -13 = -13
2x = -13

Divide each side by '2'.
x = -6.5

Simplifying
x = -6.5
Solution
x = {4, -6.5}

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