x^2+26x=11x^2+16

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Solution for x^2+26x=11x^2+16 equation: 


Simplifying
x2 + 26x = 11x2 + 16

Reorder the terms:
26x + x2 = 11x2 + 16

Reorder the terms:
26x + x2 = 16 + 11x2

Solving
26x + x2 = 16 + 11x2

Solving for variable 'x'.

Reorder the terms:
-16 + 26x + x2 + -11x2 = 16 + 11x2 + -16 + -11x2

Combine like terms: x2 + -11x2 = -10x2
-16 + 26x + -10x2 = 16 + 11x2 + -16 + -11x2

Reorder the terms:
-16 + 26x + -10x2 = 16 + -16 + 11x2 + -11x2

Combine like terms: 16 + -16 = 0
-16 + 26x + -10x2 = 0 + 11x2 + -11x2
-16 + 26x + -10x2 = 11x2 + -11x2

Combine like terms: 11x2 + -11x2 = 0
-16 + 26x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 13x + -5x2) = 0

Factor a trinomial.
2((-8 + 5x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + 5x)' equal to zero and attempt to solve:

Simplifying
-8 + 5x = 0

Solving
-8 + 5x = 0

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

Add '8' to each side of the equation.
-8 + 8 + 5x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 5x = 0 + 8
5x = 0 + 8

Combine like terms: 0 + 8 = 8
5x = 8

Divide each side by '5'.
x = 1.6

Simplifying
x = 1.6

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 = {1.6, 1}

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