7x^2+24x+24=4x^2+12x+15

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Solution for 7x^2+24x+24=4x^2+12x+15 equation: 


Simplifying
7x2 + 24x + 24 = 4x2 + 12x + 15

Reorder the terms:
24 + 24x + 7x2 = 4x2 + 12x + 15

Reorder the terms:
24 + 24x + 7x2 = 15 + 12x + 4x2

Solving
24 + 24x + 7x2 = 15 + 12x + 4x2

Solving for variable 'x'.

Reorder the terms:
24 + -15 + 24x + -12x + 7x2 + -4x2 = 15 + 12x + 4x2 + -15 + -12x + -4x2

Combine like terms: 24 + -15 = 9
9 + 24x + -12x + 7x2 + -4x2 = 15 + 12x + 4x2 + -15 + -12x + -4x2

Combine like terms: 24x + -12x = 12x
9 + 12x + 7x2 + -4x2 = 15 + 12x + 4x2 + -15 + -12x + -4x2

Combine like terms: 7x2 + -4x2 = 3x2
9 + 12x + 3x2 = 15 + 12x + 4x2 + -15 + -12x + -4x2

Reorder the terms:
9 + 12x + 3x2 = 15 + -15 + 12x + -12x + 4x2 + -4x2

Combine like terms: 15 + -15 = 0
9 + 12x + 3x2 = 0 + 12x + -12x + 4x2 + -4x2
9 + 12x + 3x2 = 12x + -12x + 4x2 + -4x2

Combine like terms: 12x + -12x = 0
9 + 12x + 3x2 = 0 + 4x2 + -4x2
9 + 12x + 3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
9 + 12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 4x + x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

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 = {-3, -1}

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