7x^2+12x+8=5x^2+7x+8

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Solution for 7x^2+12x+8=5x^2+7x+8 equation: 


Simplifying
7x2 + 12x + 8 = 5x2 + 7x + 8

Reorder the terms:
8 + 12x + 7x2 = 5x2 + 7x + 8

Reorder the terms:
8 + 12x + 7x2 = 8 + 7x + 5x2

Add '-8' to each side of the equation.
8 + 12x + -8 + 7x2 = 8 + 7x + -8 + 5x2

Reorder the terms:
8 + -8 + 12x + 7x2 = 8 + 7x + -8 + 5x2

Combine like terms: 8 + -8 = 0
0 + 12x + 7x2 = 8 + 7x + -8 + 5x2
12x + 7x2 = 8 + 7x + -8 + 5x2

Reorder the terms:
12x + 7x2 = 8 + -8 + 7x + 5x2

Combine like terms: 8 + -8 = 0
12x + 7x2 = 0 + 7x + 5x2
12x + 7x2 = 7x + 5x2

Solving
12x + 7x2 = 7x + 5x2

Solving for variable 'x'.

Reorder the terms:
12x + -7x + 7x2 + -5x2 = 7x + 5x2 + -7x + -5x2

Combine like terms: 12x + -7x = 5x
5x + 7x2 + -5x2 = 7x + 5x2 + -7x + -5x2

Combine like terms: 7x2 + -5x2 = 2x2
5x + 2x2 = 7x + 5x2 + -7x + -5x2

Reorder the terms:
5x + 2x2 = 7x + -7x + 5x2 + -5x2

Combine like terms: 7x + -7x = 0
5x + 2x2 = 0 + 5x2 + -5x2
5x + 2x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
5x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + 2x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {0, -2.5}

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