7(x^2+2x)=2(x^2+24)

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Solution for 7(x^2+2x)=2(x^2+24) equation: 


Simplifying
7(x2 + 2x) = 2(x2 + 24)

Reorder the terms:
7(2x + x2) = 2(x2 + 24)
(2x * 7 + x2 * 7) = 2(x2 + 24)
(14x + 7x2) = 2(x2 + 24)

Reorder the terms:
14x + 7x2 = 2(24 + x2)
14x + 7x2 = (24 * 2 + x2 * 2)
14x + 7x2 = (48 + 2x2)

Solving
14x + 7x2 = 48 + 2x2

Solving for variable 'x'.

Reorder the terms:
-48 + 14x + 7x2 + -2x2 = 48 + 2x2 + -48 + -2x2

Combine like terms: 7x2 + -2x2 = 5x2
-48 + 14x + 5x2 = 48 + 2x2 + -48 + -2x2

Reorder the terms:
-48 + 14x + 5x2 = 48 + -48 + 2x2 + -2x2

Combine like terms: 48 + -48 = 0
-48 + 14x + 5x2 = 0 + 2x2 + -2x2
-48 + 14x + 5x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-48 + 14x + 5x2 = 0

Factor a trinomial.
(-24 + -5x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-24 + -5x)' equal to zero and attempt to solve:

Simplifying
-24 + -5x = 0

Solving
-24 + -5x = 0

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

Add '24' to each side of the equation.
-24 + 24 + -5x = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -5x = 0 + 24
-5x = 0 + 24

Combine like terms: 0 + 24 = 24
-5x = 24

Divide each side by '-5'.
x = -4.8

Simplifying
x = -4.8

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-4.8, 2}

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