3x(x+7)=4(x^2+5x-3)

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Solution for 3x(x+7)=4(x^2+5x-3) equation: 


Simplifying
3x(x + 7) = 4(x2 + 5x + -3)

Reorder the terms:
3x(7 + x) = 4(x2 + 5x + -3)
(7 * 3x + x * 3x) = 4(x2 + 5x + -3)
(21x + 3x2) = 4(x2 + 5x + -3)

Reorder the terms:
21x + 3x2 = 4(-3 + 5x + x2)
21x + 3x2 = (-3 * 4 + 5x * 4 + x2 * 4)
21x + 3x2 = (-12 + 20x + 4x2)

Solving
21x + 3x2 = -12 + 20x + 4x2

Solving for variable 'x'.

Reorder the terms:
12 + 21x + -20x + 3x2 + -4x2 = -12 + 20x + 4x2 + 12 + -20x + -4x2

Combine like terms: 21x + -20x = 1x
12 + 1x + 3x2 + -4x2 = -12 + 20x + 4x2 + 12 + -20x + -4x2

Combine like terms: 3x2 + -4x2 = -1x2
12 + 1x + -1x2 = -12 + 20x + 4x2 + 12 + -20x + -4x2

Reorder the terms:
12 + 1x + -1x2 = -12 + 12 + 20x + -20x + 4x2 + -4x2

Combine like terms: -12 + 12 = 0
12 + 1x + -1x2 = 0 + 20x + -20x + 4x2 + -4x2
12 + 1x + -1x2 = 20x + -20x + 4x2 + -4x2

Combine like terms: 20x + -20x = 0
12 + 1x + -1x2 = 0 + 4x2 + -4x2
12 + 1x + -1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
12 + 1x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(3 + x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {4, -3}

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