3x(x+2)+4(2x-1)=5(x-2)

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Solution for 3x(x+2)+4(2x-1)=5(x-2) equation:


Simplifying
3x(x + 2) + 4(2x + -1) = 5(x + -2)

Reorder the terms:
3x(2 + x) + 4(2x + -1) = 5(x + -2)
(2 * 3x + x * 3x) + 4(2x + -1) = 5(x + -2)
(6x + 3x2) + 4(2x + -1) = 5(x + -2)

Reorder the terms:
6x + 3x2 + 4(-1 + 2x) = 5(x + -2)
6x + 3x2 + (-1 * 4 + 2x * 4) = 5(x + -2)
6x + 3x2 + (-4 + 8x) = 5(x + -2)

Reorder the terms:
-4 + 6x + 8x + 3x2 = 5(x + -2)

Combine like terms: 6x + 8x = 14x
-4 + 14x + 3x2 = 5(x + -2)

Reorder the terms:
-4 + 14x + 3x2 = 5(-2 + x)
-4 + 14x + 3x2 = (-2 * 5 + x * 5)
-4 + 14x + 3x2 = (-10 + 5x)

Solving
-4 + 14x + 3x2 = -10 + 5x

Solving for variable 'x'.

Reorder the terms:
-4 + 10 + 14x + -5x + 3x2 = -10 + 5x + 10 + -5x

Combine like terms: -4 + 10 = 6
6 + 14x + -5x + 3x2 = -10 + 5x + 10 + -5x

Combine like terms: 14x + -5x = 9x
6 + 9x + 3x2 = -10 + 5x + 10 + -5x

Reorder the terms:
6 + 9x + 3x2 = -10 + 10 + 5x + -5x

Combine like terms: -10 + 10 = 0
6 + 9x + 3x2 = 0 + 5x + -5x
6 + 9x + 3x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
6 + 9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 3x + x2) = 0

Factor a trinomial.
3((2 + x)(1 + x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Subproblem 2

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

Solution

x = {-2, -1}

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