2x^2+5x-3=7x+9

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Solution for 2x^2+5x-3=7x+9 equation: 


Simplifying
2x2 + 5x + -3 = 7x + 9

Reorder the terms:
-3 + 5x + 2x2 = 7x + 9

Reorder the terms:
-3 + 5x + 2x2 = 9 + 7x

Solving
-3 + 5x + 2x2 = 9 + 7x

Solving for variable 'x'.

Reorder the terms:
-3 + -9 + 5x + -7x + 2x2 = 9 + 7x + -9 + -7x

Combine like terms: -3 + -9 = -12
-12 + 5x + -7x + 2x2 = 9 + 7x + -9 + -7x

Combine like terms: 5x + -7x = -2x
-12 + -2x + 2x2 = 9 + 7x + -9 + -7x

Reorder the terms:
-12 + -2x + 2x2 = 9 + -9 + 7x + -7x

Combine like terms: 9 + -9 = 0
-12 + -2x + 2x2 = 0 + 7x + -7x
-12 + -2x + 2x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-12 + -2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1x + x2) = 0

Factor a trinomial.
2((-2 + -1x)(3 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
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
Solution
x = {-2, 3}

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