-3x(x-4)+15=-5(x-7)-10

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Solution for -3x(x-4)+15=-5(x-7)-10 equation: 


Simplifying
-3x(x + -4) + 15 = -5(x + -7) + -10

Reorder the terms:
-3x(-4 + x) + 15 = -5(x + -7) + -10
(-4 * -3x + x * -3x) + 15 = -5(x + -7) + -10
(12x + -3x2) + 15 = -5(x + -7) + -10

Reorder the terms:
15 + 12x + -3x2 = -5(x + -7) + -10

Reorder the terms:
15 + 12x + -3x2 = -5(-7 + x) + -10
15 + 12x + -3x2 = (-7 * -5 + x * -5) + -10
15 + 12x + -3x2 = (35 + -5x) + -10

Reorder the terms:
15 + 12x + -3x2 = 35 + -10 + -5x

Combine like terms: 35 + -10 = 25
15 + 12x + -3x2 = 25 + -5x

Solving
15 + 12x + -3x2 = 25 + -5x

Solving for variable 'x'.

Reorder the terms:
15 + -25 + 12x + 5x + -3x2 = 25 + -5x + -25 + 5x

Combine like terms: 15 + -25 = -10
-10 + 12x + 5x + -3x2 = 25 + -5x + -25 + 5x

Combine like terms: 12x + 5x = 17x
-10 + 17x + -3x2 = 25 + -5x + -25 + 5x

Reorder the terms:
-10 + 17x + -3x2 = 25 + -25 + -5x + 5x

Combine like terms: 25 + -25 = 0
-10 + 17x + -3x2 = 0 + -5x + 5x
-10 + 17x + -3x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-10 + 17x + -3x2 = 0

Factor a trinomial.
(-5 + x)(2 + -3x) = 0


Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

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

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

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

Simplifying
x = 5

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

Simplifying
2 + -3x = 0

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

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {5, 0.6666666667}

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