4x^2+24x^2+36x^2=4x^2+16x+16

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Solution for 4x^2+24x^2+36x^2=4x^2+16x+16 equation: 


Simplifying
4x2 + 24x2 + 36x2 = 4x2 + 16x + 16

Combine like terms: 4x2 + 24x2 = 28x2
28x2 + 36x2 = 4x2 + 16x + 16

Combine like terms: 28x2 + 36x2 = 64x2
64x2 = 4x2 + 16x + 16

Reorder the terms:
64x2 = 16 + 16x + 4x2

Solving
64x2 = 16 + 16x + 4x2

Solving for variable 'x'.

Reorder the terms:
-16 + -16x + 64x2 + -4x2 = 16 + 16x + 4x2 + -16 + -16x + -4x2

Combine like terms: 64x2 + -4x2 = 60x2
-16 + -16x + 60x2 = 16 + 16x + 4x2 + -16 + -16x + -4x2

Reorder the terms:
-16 + -16x + 60x2 = 16 + -16 + 16x + -16x + 4x2 + -4x2

Combine like terms: 16 + -16 = 0
-16 + -16x + 60x2 = 0 + 16x + -16x + 4x2 + -4x2
-16 + -16x + 60x2 = 16x + -16x + 4x2 + -4x2

Combine like terms: 16x + -16x = 0
-16 + -16x + 60x2 = 0 + 4x2 + -4x2
-16 + -16x + 60x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-16 + -16x + 60x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + -4x + 15x2) = 0

Factor a trinomial.
4((-2 + -5x)(2 + -3x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-2 + -5x)' equal to zero and attempt to solve:

Simplifying
-2 + -5x = 0

Solving
-2 + -5x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5x = 0 + 2

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

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

Divide each side by '-5'.
x = -0.4

Simplifying
x = -0.4

Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-0.4, 0.6666666667}

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