7x^2-8x+3=18+3x-5x^2

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Solution for 7x^2-8x+3=18+3x-5x^2 equation: 


Simplifying
7x2 + -8x + 3 = 18 + 3x + -5x2

Reorder the terms:
3 + -8x + 7x2 = 18 + 3x + -5x2

Solving
3 + -8x + 7x2 = 18 + 3x + -5x2

Solving for variable 'x'.

Reorder the terms:
3 + -18 + -8x + -3x + 7x2 + 5x2 = 18 + 3x + -5x2 + -18 + -3x + 5x2

Combine like terms: 3 + -18 = -15
-15 + -8x + -3x + 7x2 + 5x2 = 18 + 3x + -5x2 + -18 + -3x + 5x2

Combine like terms: -8x + -3x = -11x
-15 + -11x + 7x2 + 5x2 = 18 + 3x + -5x2 + -18 + -3x + 5x2

Combine like terms: 7x2 + 5x2 = 12x2
-15 + -11x + 12x2 = 18 + 3x + -5x2 + -18 + -3x + 5x2

Reorder the terms:
-15 + -11x + 12x2 = 18 + -18 + 3x + -3x + -5x2 + 5x2

Combine like terms: 18 + -18 = 0
-15 + -11x + 12x2 = 0 + 3x + -3x + -5x2 + 5x2
-15 + -11x + 12x2 = 3x + -3x + -5x2 + 5x2

Combine like terms: 3x + -3x = 0
-15 + -11x + 12x2 = 0 + -5x2 + 5x2
-15 + -11x + 12x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-15 + -11x + 12x2 = 0

Factor a trinomial.
(-3 + -4x)(5 + -3x) = 0


Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 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 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-0.75, 1.666666667}

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