x^2=7x-10sin(x)

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Solution for x^2=7x-10sin(x) equation: 


Simplifying
x2 = 7x + -10sin(x)

Multiply ins * x
x2 = 7x + -10insx

Reorder the terms:
x2 = -10insx + 7x

Solving
x2 = -10insx + 7x

Solving for variable 'x'.

Reorder the terms:
10insx + -7x + x2 = -10insx + 7x + 10insx + -7x

Reorder the terms:
10insx + -7x + x2 = -10insx + 10insx + 7x + -7x

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(10ins + -7 + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(10ins + -7 + x)' equal to zero and attempt to solve:

Simplifying
10ins + -7 + x = 0

Reorder the terms:
-7 + 10ins + x = 0

Solving
-7 + 10ins + x = 0

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

Add '7' to each side of the equation.
-7 + 10ins + 7 + x = 0 + 7

Reorder the terms:
-7 + 7 + 10ins + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 10ins + x = 0 + 7
10ins + x = 0 + 7

Combine like terms: 0 + 7 = 7
10ins + x = 7

Add '-10ins' to each side of the equation.
10ins + -10ins + x = 7 + -10ins

Combine like terms: 10ins + -10ins = 0
0 + x = 7 + -10ins
x = 7 + -10ins

Simplifying
x = 7 + -10ins
Solution
x = {0, 7 + -10ins}

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