x^2-9=4x^2-16x+7

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Solution for x^2-9=4x^2-16x+7 equation: 


Simplifying
x2 + -9 = 4x2 + -16x + 7

Reorder the terms:
-9 + x2 = 4x2 + -16x + 7

Reorder the terms:
-9 + x2 = 7 + -16x + 4x2

Solving
-9 + x2 = 7 + -16x + 4x2

Solving for variable 'x'.

Reorder the terms:
-9 + -7 + 16x + x2 + -4x2 = 7 + -16x + 4x2 + -7 + 16x + -4x2

Combine like terms: -9 + -7 = -16
-16 + 16x + x2 + -4x2 = 7 + -16x + 4x2 + -7 + 16x + -4x2

Combine like terms: x2 + -4x2 = -3x2
-16 + 16x + -3x2 = 7 + -16x + 4x2 + -7 + 16x + -4x2

Reorder the terms:
-16 + 16x + -3x2 = 7 + -7 + -16x + 16x + 4x2 + -4x2

Combine like terms: 7 + -7 = 0
-16 + 16x + -3x2 = 0 + -16x + 16x + 4x2 + -4x2
-16 + 16x + -3x2 = -16x + 16x + 4x2 + -4x2

Combine like terms: -16x + 16x = 0
-16 + 16x + -3x2 = 0 + 4x2 + -4x2
-16 + 16x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-16 + 16x + -3x2 = 0

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


Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {4, 1.333333333}

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