15x^2+(x+10)(x+10)=100

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Solution for 15x^2+(x+10)(x+10)=100 equation: 


Simplifying
15x2 + (x + 10)(x + 10) = 100

Reorder the terms:
15x2 + (10 + x)(x + 10) = 100

Reorder the terms:
15x2 + (10 + x)(10 + x) = 100

Multiply (10 + x) * (10 + x)
15x2 + (10(10 + x) + x(10 + x)) = 100
15x2 + ((10 * 10 + x * 10) + x(10 + x)) = 100
15x2 + ((100 + 10x) + x(10 + x)) = 100
15x2 + (100 + 10x + (10 * x + x * x)) = 100
15x2 + (100 + 10x + (10x + x2)) = 100

Combine like terms: 10x + 10x = 20x
15x2 + (100 + 20x + x2) = 100

Reorder the terms:
100 + 20x + 15x2 + x2 = 100

Combine like terms: 15x2 + x2 = 16x2
100 + 20x + 16x2 = 100

Add '-100' to each side of the equation.
100 + 20x + -100 + 16x2 = 100 + -100

Reorder the terms:
100 + -100 + 20x + 16x2 = 100 + -100

Combine like terms: 100 + -100 = 0
0 + 20x + 16x2 = 100 + -100
20x + 16x2 = 100 + -100

Combine like terms: 100 + -100 = 0
20x + 16x2 = 0

Solving
20x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(5 + 4x) = 0

Ignore the factor 4.

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 '(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 = {0, -1.25}

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