5(x^2)+(2x)=2(x^2)-(8x)+48

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Solution for 5(x^2)+(2x)=2(x^2)-(8x)+48 equation:


Simplifying
5(x2) + (2x) = 2(x2) + -1(8x) + 48

Reorder the terms:
(2x) + 5x2 = 2(x2) + -1(8x) + 48

Remove parenthesis around (8x)
(2x) + 5x2 = 2x2 + -1 * 8x + 48

Multiply -1 * 8
(2x) + 5x2 = 2x2 + -8x + 48

Reorder the terms:
(2x) + 5x2 = 48 + -8x + 2x2

Solving
(2x) + 5x2 = 48 + -8x + 2x2

Solving for variable 'x'.

Reorder the terms:
-48 + (2x) + 8x + 5x2 + -2x2 = 48 + -8x + 2x2 + -48 + 8x + -2x2

Combine like terms: (2x) + 8x = 10x
-48 + 10x + 5x2 + -2x2 = 48 + -8x + 2x2 + -48 + 8x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-48 + 10x + 3x2 = 48 + -8x + 2x2 + -48 + 8x + -2x2

Reorder the terms:
-48 + 10x + 3x2 = 48 + -48 + -8x + 8x + 2x2 + -2x2

Combine like terms: 48 + -48 = 0
-48 + 10x + 3x2 = 0 + -8x + 8x + 2x2 + -2x2
-48 + 10x + 3x2 = -8x + 8x + 2x2 + -2x2

Combine like terms: -8x + 8x = 0
-48 + 10x + 3x2 = 0 + 2x2 + -2x2
-48 + 10x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-48 + 10x + 3x2 = 0

Factor a trinomial.
(-6 + -1x)(8 + -3x) = 0

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

Subproblem 2

Set the factor '(8 + -3x)' equal to zero and attempt to solve: Simplifying 8 + -3x = 0 Solving 8 + -3x = 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 + -3x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3x = 0 + -8 -3x = 0 + -8 Combine like terms: 0 + -8 = -8 -3x = -8 Divide each side by '-3'. x = 2.666666667 Simplifying x = 2.666666667

Solution

x = {-6, 2.666666667}

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