2x^2+5x-3=2(x+3)

Solution for 2x^2+5x-3=2(x+3) equation:

Simplifying
2x2 + 5x + -3 = 2(x + 3)

Reorder the terms:
-3 + 5x + 2x2 = 2(x + 3)

Reorder the terms:
-3 + 5x + 2x2 = 2(3 + x)
-3 + 5x + 2x2 = (3 * 2 + x * 2)
-3 + 5x + 2x2 = (6 + 2x)

Solving
-3 + 5x + 2x2 = 6 + 2x

Solving for variable 'x'.

Reorder the terms:
-3 + -6 + 5x + -2x + 2x2 = 6 + 2x + -6 + -2x

Combine like terms: -3 + -6 = -9
-9 + 5x + -2x + 2x2 = 6 + 2x + -6 + -2x

Combine like terms: 5x + -2x = 3x
-9 + 3x + 2x2 = 6 + 2x + -6 + -2x

Reorder the terms:
-9 + 3x + 2x2 = 6 + -6 + 2x + -2x

Combine like terms: 6 + -6 = 0
-9 + 3x + 2x2 = 0 + 2x + -2x
-9 + 3x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-9 + 3x + 2x2 = 0

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

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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-3, 1.5}