5x(2x-3)+10=8-3(4x-2)

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Solution for 5x(2x-3)+10=8-3(4x-2) equation: 


Simplifying
5x(2x + -3) + 10 = 8 + -3(4x + -2)

Reorder the terms:
5x(-3 + 2x) + 10 = 8 + -3(4x + -2)
(-3 * 5x + 2x * 5x) + 10 = 8 + -3(4x + -2)
(-15x + 10x2) + 10 = 8 + -3(4x + -2)

Reorder the terms:
10 + -15x + 10x2 = 8 + -3(4x + -2)

Reorder the terms:
10 + -15x + 10x2 = 8 + -3(-2 + 4x)
10 + -15x + 10x2 = 8 + (-2 * -3 + 4x * -3)
10 + -15x + 10x2 = 8 + (6 + -12x)

Combine like terms: 8 + 6 = 14
10 + -15x + 10x2 = 14 + -12x

Solving
10 + -15x + 10x2 = 14 + -12x

Solving for variable 'x'.

Reorder the terms:
10 + -14 + -15x + 12x + 10x2 = 14 + -12x + -14 + 12x

Combine like terms: 10 + -14 = -4
-4 + -15x + 12x + 10x2 = 14 + -12x + -14 + 12x

Combine like terms: -15x + 12x = -3x
-4 + -3x + 10x2 = 14 + -12x + -14 + 12x

Reorder the terms:
-4 + -3x + 10x2 = 14 + -14 + -12x + 12x

Combine like terms: 14 + -14 = 0
-4 + -3x + 10x2 = 0 + -12x + 12x
-4 + -3x + 10x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
-4 + -3x + 10x2 = 0

Factor a trinomial.
(-1 + -2x)(4 + -5x) = 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 '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x = 0 + -4
-5x = 0 + -4

Combine like terms: 0 + -4 = -4
-5x = -4

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8
Solution
x = {-0.5, 0.8}

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