3(x-5)(2x+1)=(6x-10)(6x+3)

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Solution for 3(x-5)(2x+1)=(6x-10)(6x+3) equation:


Simplifying
3(x + -5)(2x + 1) = (6x + -10)(6x + 3)

Reorder the terms:
3(-5 + x)(2x + 1) = (6x + -10)(6x + 3)

Reorder the terms:
3(-5 + x)(1 + 2x) = (6x + -10)(6x + 3)

Multiply (-5 + x) * (1 + 2x)
3(-5(1 + 2x) + x(1 + 2x)) = (6x + -10)(6x + 3)
3((1 * -5 + 2x * -5) + x(1 + 2x)) = (6x + -10)(6x + 3)
3((-5 + -10x) + x(1 + 2x)) = (6x + -10)(6x + 3)
3(-5 + -10x + (1 * x + 2x * x)) = (6x + -10)(6x + 3)
3(-5 + -10x + (1x + 2x2)) = (6x + -10)(6x + 3)

Combine like terms: -10x + 1x = -9x
3(-5 + -9x + 2x2) = (6x + -10)(6x + 3)
(-5 * 3 + -9x * 3 + 2x2 * 3) = (6x + -10)(6x + 3)
(-15 + -27x + 6x2) = (6x + -10)(6x + 3)

Reorder the terms:
-15 + -27x + 6x2 = (-10 + 6x)(6x + 3)

Reorder the terms:
-15 + -27x + 6x2 = (-10 + 6x)(3 + 6x)

Multiply (-10 + 6x) * (3 + 6x)
-15 + -27x + 6x2 = (-10(3 + 6x) + 6x * (3 + 6x))
-15 + -27x + 6x2 = ((3 * -10 + 6x * -10) + 6x * (3 + 6x))
-15 + -27x + 6x2 = ((-30 + -60x) + 6x * (3 + 6x))
-15 + -27x + 6x2 = (-30 + -60x + (3 * 6x + 6x * 6x))
-15 + -27x + 6x2 = (-30 + -60x + (18x + 36x2))

Combine like terms: -60x + 18x = -42x
-15 + -27x + 6x2 = (-30 + -42x + 36x2)

Solving
-15 + -27x + 6x2 = -30 + -42x + 36x2

Solving for variable 'x'.

Reorder the terms:
-15 + 30 + -27x + 42x + 6x2 + -36x2 = -30 + -42x + 36x2 + 30 + 42x + -36x2

Combine like terms: -15 + 30 = 15
15 + -27x + 42x + 6x2 + -36x2 = -30 + -42x + 36x2 + 30 + 42x + -36x2

Combine like terms: -27x + 42x = 15x
15 + 15x + 6x2 + -36x2 = -30 + -42x + 36x2 + 30 + 42x + -36x2

Combine like terms: 6x2 + -36x2 = -30x2
15 + 15x + -30x2 = -30 + -42x + 36x2 + 30 + 42x + -36x2

Reorder the terms:
15 + 15x + -30x2 = -30 + 30 + -42x + 42x + 36x2 + -36x2

Combine like terms: -30 + 30 = 0
15 + 15x + -30x2 = 0 + -42x + 42x + 36x2 + -36x2
15 + 15x + -30x2 = -42x + 42x + 36x2 + -36x2

Combine like terms: -42x + 42x = 0
15 + 15x + -30x2 = 0 + 36x2 + -36x2
15 + 15x + -30x2 = 36x2 + -36x2

Combine like terms: 36x2 + -36x2 = 0
15 + 15x + -30x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(1 + x + -2x2) = 0

Factor a trinomial.
15((1 + -1x)(1 + 2x)) = 0

Ignore the factor 15.

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

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 2
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
Solution
x = {1, -0.5}

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