(6x+5)(x-3)=-2x(7x+5)+x-12

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Solution for (6x+5)(x-3)=-2x(7x+5)+x-12 equation:


Simplifying
(6x + 5)(x + -3) = -2x(7x + 5) + x + -12

Reorder the terms:
(5 + 6x)(x + -3) = -2x(7x + 5) + x + -12

Reorder the terms:
(5 + 6x)(-3 + x) = -2x(7x + 5) + x + -12

Multiply (5 + 6x) * (-3 + x)
(5(-3 + x) + 6x * (-3 + x)) = -2x(7x + 5) + x + -12
((-3 * 5 + x * 5) + 6x * (-3 + x)) = -2x(7x + 5) + x + -12
((-15 + 5x) + 6x * (-3 + x)) = -2x(7x + 5) + x + -12
(-15 + 5x + (-3 * 6x + x * 6x)) = -2x(7x + 5) + x + -12
(-15 + 5x + (-18x + 6x2)) = -2x(7x + 5) + x + -12

Combine like terms: 5x + -18x = -13x
(-15 + -13x + 6x2) = -2x(7x + 5) + x + -12

Reorder the terms:
-15 + -13x + 6x2 = -2x(5 + 7x) + x + -12
-15 + -13x + 6x2 = (5 * -2x + 7x * -2x) + x + -12
-15 + -13x + 6x2 = (-10x + -14x2) + x + -12

Reorder the terms:
-15 + -13x + 6x2 = -12 + -10x + x + -14x2

Combine like terms: -10x + x = -9x
-15 + -13x + 6x2 = -12 + -9x + -14x2

Solving
-15 + -13x + 6x2 = -12 + -9x + -14x2

Solving for variable 'x'.

Reorder the terms:
-15 + 12 + -13x + 9x + 6x2 + 14x2 = -12 + -9x + -14x2 + 12 + 9x + 14x2

Combine like terms: -15 + 12 = -3
-3 + -13x + 9x + 6x2 + 14x2 = -12 + -9x + -14x2 + 12 + 9x + 14x2

Combine like terms: -13x + 9x = -4x
-3 + -4x + 6x2 + 14x2 = -12 + -9x + -14x2 + 12 + 9x + 14x2

Combine like terms: 6x2 + 14x2 = 20x2
-3 + -4x + 20x2 = -12 + -9x + -14x2 + 12 + 9x + 14x2

Reorder the terms:
-3 + -4x + 20x2 = -12 + 12 + -9x + 9x + -14x2 + 14x2

Combine like terms: -12 + 12 = 0
-3 + -4x + 20x2 = 0 + -9x + 9x + -14x2 + 14x2
-3 + -4x + 20x2 = -9x + 9x + -14x2 + 14x2

Combine like terms: -9x + 9x = 0
-3 + -4x + 20x2 = 0 + -14x2 + 14x2
-3 + -4x + 20x2 = -14x2 + 14x2

Combine like terms: -14x2 + 14x2 = 0
-3 + -4x + 20x2 = 0

Factor a trinomial.
(-3 + -10x)(1 + -2x) = 0

Subproblem 1

Set the factor '(-3 + -10x)' equal to zero and attempt to solve: Simplifying -3 + -10x = 0 Solving -3 + -10x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -10x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -10x = 0 + 3 -10x = 0 + 3 Combine like terms: 0 + 3 = 3 -10x = 3 Divide each side by '-10'. x = -0.3 Simplifying x = -0.3

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 = {-0.3, 0.5}

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