2x^2-48x=-7x^2-4x-32

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Solution for 2x^2-48x=-7x^2-4x-32 equation: 


Simplifying
2x2 + -48x = -7x2 + -4x + -32

Reorder the terms:
-48x + 2x2 = -7x2 + -4x + -32

Reorder the terms:
-48x + 2x2 = -32 + -4x + -7x2

Solving
-48x + 2x2 = -32 + -4x + -7x2

Solving for variable 'x'.

Reorder the terms:
32 + -48x + 4x + 2x2 + 7x2 = -32 + -4x + -7x2 + 32 + 4x + 7x2

Combine like terms: -48x + 4x = -44x
32 + -44x + 2x2 + 7x2 = -32 + -4x + -7x2 + 32 + 4x + 7x2

Combine like terms: 2x2 + 7x2 = 9x2
32 + -44x + 9x2 = -32 + -4x + -7x2 + 32 + 4x + 7x2

Reorder the terms:
32 + -44x + 9x2 = -32 + 32 + -4x + 4x + -7x2 + 7x2

Combine like terms: -32 + 32 = 0
32 + -44x + 9x2 = 0 + -4x + 4x + -7x2 + 7x2
32 + -44x + 9x2 = -4x + 4x + -7x2 + 7x2

Combine like terms: -4x + 4x = 0
32 + -44x + 9x2 = 0 + -7x2 + 7x2
32 + -44x + 9x2 = -7x2 + 7x2

Combine like terms: -7x2 + 7x2 = 0
32 + -44x + 9x2 = 0

Factor a trinomial.
(8 + -9x)(4 + -1x) = 0


Subproblem 1
Set the factor '(8 + -9x)' equal to zero and attempt to solve:

Simplifying
8 + -9x = 0

Solving
8 + -9x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -9x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -9x = 0 + -8
-9x = 0 + -8

Combine like terms: 0 + -8 = -8
-9x = -8

Divide each side by '-9'.
x = 0.8888888889

Simplifying
x = 0.8888888889

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0.8888888889, 4}

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