x(4x+7)+20=x(3x-2)

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Solution for x(4x+7)+20=x(3x-2) equation: 


Simplifying
x(4x + 7) + 20 = x(3x + -2)

Reorder the terms:
x(7 + 4x) + 20 = x(3x + -2)
(7 * x + 4x * x) + 20 = x(3x + -2)
(7x + 4x2) + 20 = x(3x + -2)

Reorder the terms:
20 + 7x + 4x2 = x(3x + -2)

Reorder the terms:
20 + 7x + 4x2 = x(-2 + 3x)
20 + 7x + 4x2 = (-2 * x + 3x * x)
20 + 7x + 4x2 = (-2x + 3x2)

Solving
20 + 7x + 4x2 = -2x + 3x2

Solving for variable 'x'.

Reorder the terms:
20 + 7x + 2x + 4x2 + -3x2 = -2x + 3x2 + 2x + -3x2

Combine like terms: 7x + 2x = 9x
20 + 9x + 4x2 + -3x2 = -2x + 3x2 + 2x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
20 + 9x + 1x2 = -2x + 3x2 + 2x + -3x2

Reorder the terms:
20 + 9x + 1x2 = -2x + 2x + 3x2 + -3x2

Combine like terms: -2x + 2x = 0
20 + 9x + 1x2 = 0 + 3x2 + -3x2
20 + 9x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
20 + 9x + 1x2 = 0

Factor a trinomial.
(5 + x)(4 + x) = 0


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

Simplifying
5 + x = 0

Solving
5 + x = 0

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

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

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

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

Simplifying
x = -5

Subproblem 2
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
Solution
x = {-5, -4}

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