5x^2+7x=-3x+15

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Solution for 5x^2+7x=-3x+15 equation: 


Simplifying
5x2 + 7x = -3x + 15

Reorder the terms:
7x + 5x2 = -3x + 15

Reorder the terms:
7x + 5x2 = 15 + -3x

Solving
7x + 5x2 = 15 + -3x

Solving for variable 'x'.

Reorder the terms:
-15 + 7x + 3x + 5x2 = 15 + -3x + -15 + 3x

Combine like terms: 7x + 3x = 10x
-15 + 10x + 5x2 = 15 + -3x + -15 + 3x

Reorder the terms:
-15 + 10x + 5x2 = 15 + -15 + -3x + 3x

Combine like terms: 15 + -15 = 0
-15 + 10x + 5x2 = 0 + -3x + 3x
-15 + 10x + 5x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-15 + 10x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + 2x + x2) = 0

Factor a trinomial.
5((-3 + -1x)(1 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-3, 1}

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