15x^2=10x^2+7x^2-2(10)(7)cosx

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Solution for 15x^2=10x^2+7x^2-2(10)(7)cosx equation: 


Simplifying
15x2 = 10x2 + 7x2 + -2(10)(7) * cosx

Multiply -2 * 10
15x2 = 10x2 + 7x2 + -20 * 7cosx

Multiply -20 * 7
15x2 = 10x2 + 7x2 + -140cosx

Reorder the terms:
15x2 = -140cosx + 10x2 + 7x2

Combine like terms: 10x2 + 7x2 = 17x2
15x2 = -140cosx + 17x2

Solving
15x2 = -140cosx + 17x2

Solving for variable 'x'.

Reorder the terms:
140cosx + 15x2 + -17x2 = -140cosx + 17x2 + 140cosx + -17x2

Combine like terms: 15x2 + -17x2 = -2x2
140cosx + -2x2 = -140cosx + 17x2 + 140cosx + -17x2

Reorder the terms:
140cosx + -2x2 = -140cosx + 140cosx + 17x2 + -17x2

Combine like terms: -140cosx + 140cosx = 0
140cosx + -2x2 = 0 + 17x2 + -17x2
140cosx + -2x2 = 17x2 + -17x2

Combine like terms: 17x2 + -17x2 = 0
140cosx + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(70cos + -1x) = 0

Ignore the factor 2.

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 '(70cos + -1x)' equal to zero and attempt to solve:

Simplifying
70cos + -1x = 0

Solving
70cos + -1x = 0

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

Add '-70cos' to each side of the equation.
70cos + -70cos + -1x = 0 + -70cos

Combine like terms: 70cos + -70cos = 0
0 + -1x = 0 + -70cos
-1x = 0 + -70cos
Remove the zero:
-1x = -70cos

Divide each side by '-1'.
x = 70cos

Simplifying
x = 70cos
Solution
x = {0, 70cos}

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