(3x+2)(4x-3)-10x(x+1)=0

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Solution for (3x+2)(4x-3)-10x(x+1)=0 equation:


Simplifying
(3x + 2)(4x + -3) + -10x(x + 1) = 0

Reorder the terms:
(2 + 3x)(4x + -3) + -10x(x + 1) = 0

Reorder the terms:
(2 + 3x)(-3 + 4x) + -10x(x + 1) = 0

Multiply (2 + 3x) * (-3 + 4x)
(2(-3 + 4x) + 3x * (-3 + 4x)) + -10x(x + 1) = 0
((-3 * 2 + 4x * 2) + 3x * (-3 + 4x)) + -10x(x + 1) = 0
((-6 + 8x) + 3x * (-3 + 4x)) + -10x(x + 1) = 0
(-6 + 8x + (-3 * 3x + 4x * 3x)) + -10x(x + 1) = 0
(-6 + 8x + (-9x + 12x2)) + -10x(x + 1) = 0

Combine like terms: 8x + -9x = -1x
(-6 + -1x + 12x2) + -10x(x + 1) = 0

Reorder the terms:
-6 + -1x + 12x2 + -10x(1 + x) = 0
-6 + -1x + 12x2 + (1 * -10x + x * -10x) = 0
-6 + -1x + 12x2 + (-10x + -10x2) = 0

Reorder the terms:
-6 + -1x + -10x + 12x2 + -10x2 = 0

Combine like terms: -1x + -10x = -11x
-6 + -11x + 12x2 + -10x2 = 0

Combine like terms: 12x2 + -10x2 = 2x2
-6 + -11x + 2x2 = 0

Solving
-6 + -11x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -2x)(6 + -1x) = 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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {-0.5, 6}

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