3-x(5x+8)=2+x(7x-12)

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Solution for 3-x(5x+8)=2+x(7x-12) equation: 


Simplifying
3 + -1x(5x + 8) = 2 + x(7x + -12)

Reorder the terms:
3 + -1x(8 + 5x) = 2 + x(7x + -12)
3 + (8 * -1x + 5x * -1x) = 2 + x(7x + -12)
3 + (-8x + -5x2) = 2 + x(7x + -12)

Reorder the terms:
3 + -8x + -5x2 = 2 + x(-12 + 7x)
3 + -8x + -5x2 = 2 + (-12 * x + 7x * x)
3 + -8x + -5x2 = 2 + (-12x + 7x2)

Solving
3 + -8x + -5x2 = 2 + -12x + 7x2

Solving for variable 'x'.

Reorder the terms:
3 + -2 + -8x + 12x + -5x2 + -7x2 = 2 + -12x + 7x2 + -2 + 12x + -7x2

Combine like terms: 3 + -2 = 1
1 + -8x + 12x + -5x2 + -7x2 = 2 + -12x + 7x2 + -2 + 12x + -7x2

Combine like terms: -8x + 12x = 4x
1 + 4x + -5x2 + -7x2 = 2 + -12x + 7x2 + -2 + 12x + -7x2

Combine like terms: -5x2 + -7x2 = -12x2
1 + 4x + -12x2 = 2 + -12x + 7x2 + -2 + 12x + -7x2

Reorder the terms:
1 + 4x + -12x2 = 2 + -2 + -12x + 12x + 7x2 + -7x2

Combine like terms: 2 + -2 = 0
1 + 4x + -12x2 = 0 + -12x + 12x + 7x2 + -7x2
1 + 4x + -12x2 = -12x + 12x + 7x2 + -7x2

Combine like terms: -12x + 12x = 0
1 + 4x + -12x2 = 0 + 7x2 + -7x2
1 + 4x + -12x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
1 + 4x + -12x2 = 0

Factor a trinomial.
(1 + -2x)(1 + 6x) = 0


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(1 + 6x)' equal to zero and attempt to solve:

Simplifying
1 + 6x = 0

Solving
1 + 6x = 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 + 6x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6x = 0 + -1
6x = 0 + -1

Combine like terms: 0 + -1 = -1
6x = -1

Divide each side by '6'.
x = -0.1666666667

Simplifying
x = -0.1666666667
Solution
x = {0.5, -0.1666666667}

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