2.5x^2+52x+186=-0.5x^2+4x-3

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Solution for 2.5x^2+52x+186=-0.5x^2+4x-3 equation: 


Simplifying
2.5x2 + 52x + 186 = -0.5x2 + 4x + -3

Reorder the terms:
186 + 52x + 2.5x2 = -0.5x2 + 4x + -3

Reorder the terms:
186 + 52x + 2.5x2 = -3 + 4x + -0.5x2

Solving
186 + 52x + 2.5x2 = -3 + 4x + -0.5x2

Solving for variable 'x'.

Reorder the terms:
186 + 3 + 52x + -4x + 2.5x2 + 0.5x2 = -3 + 4x + -0.5x2 + 3 + -4x + 0.5x2

Combine like terms: 186 + 3 = 189
189 + 52x + -4x + 2.5x2 + 0.5x2 = -3 + 4x + -0.5x2 + 3 + -4x + 0.5x2

Combine like terms: 52x + -4x = 48x
189 + 48x + 2.5x2 + 0.5x2 = -3 + 4x + -0.5x2 + 3 + -4x + 0.5x2

Combine like terms: 2.5x2 + 0.5x2 = 3x2
189 + 48x + 3x2 = -3 + 4x + -0.5x2 + 3 + -4x + 0.5x2

Reorder the terms:
189 + 48x + 3x2 = -3 + 3 + 4x + -4x + -0.5x2 + 0.5x2

Combine like terms: -3 + 3 = 0
189 + 48x + 3x2 = 0 + 4x + -4x + -0.5x2 + 0.5x2
189 + 48x + 3x2 = 4x + -4x + -0.5x2 + 0.5x2

Combine like terms: 4x + -4x = 0
189 + 48x + 3x2 = 0 + -0.5x2 + 0.5x2
189 + 48x + 3x2 = -0.5x2 + 0.5x2

Combine like terms: -0.5x2 + 0.5x2 = 0.0
189 + 48x + 3x2 = 0.0

Factor out the Greatest Common Factor (GCF), '3'.
3(63 + 16x + x2) = 0.0

Factor a trinomial.
3((9 + x)(7 + x)) = 0.0

Ignore the factor 3.

Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9

Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {-9, -7}

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