(2x+7)(x*x+12x-30)-5x*x=2x*x(x+1)

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Solution for (2x+7)(x*x+12x-30)-5x*x=2x*x(x+1) equation:


Simplifying
(2x + 7)(x * x + 12x + -30) + -5x * x = 2x * x(x + 1)

Reorder the terms:
(7 + 2x)(x * x + 12x + -30) + -5x * x = 2x * x(x + 1)

Multiply x * x
(7 + 2x)(x2 + 12x + -30) + -5x * x = 2x * x(x + 1)

Reorder the terms:
(7 + 2x)(-30 + 12x + x2) + -5x * x = 2x * x(x + 1)

Multiply (7 + 2x) * (-30 + 12x + x2)
(7(-30 + 12x + x2) + 2x * (-30 + 12x + x2)) + -5x * x = 2x * x(x + 1)
((-30 * 7 + 12x * 7 + x2 * 7) + 2x * (-30 + 12x + x2)) + -5x * x = 2x * x(x + 1)
((-210 + 84x + 7x2) + 2x * (-30 + 12x + x2)) + -5x * x = 2x * x(x + 1)
(-210 + 84x + 7x2 + (-30 * 2x + 12x * 2x + x2 * 2x)) + -5x * x = 2x * x(x + 1)
(-210 + 84x + 7x2 + (-60x + 24x2 + 2x3)) + -5x * x = 2x * x(x + 1)

Reorder the terms:
(-210 + 84x + -60x + 7x2 + 24x2 + 2x3) + -5x * x = 2x * x(x + 1)

Combine like terms: 84x + -60x = 24x
(-210 + 24x + 7x2 + 24x2 + 2x3) + -5x * x = 2x * x(x + 1)

Combine like terms: 7x2 + 24x2 = 31x2
(-210 + 24x + 31x2 + 2x3) + -5x * x = 2x * x(x + 1)

Multiply x * x
-210 + 24x + 31x2 + 2x3 + -5x2 = 2x * x(x + 1)

Reorder the terms:
-210 + 24x + 31x2 + -5x2 + 2x3 = 2x * x(x + 1)

Combine like terms: 31x2 + -5x2 = 26x2
-210 + 24x + 26x2 + 2x3 = 2x * x(x + 1)

Reorder the terms:
-210 + 24x + 26x2 + 2x3 = 2x * x(1 + x)

Multiply x * x
-210 + 24x + 26x2 + 2x3 = 2x2(1 + x)
-210 + 24x + 26x2 + 2x3 = (1 * 2x2 + x * 2x2)
-210 + 24x + 26x2 + 2x3 = (2x2 + 2x3)

Add '-2x3' to each side of the equation.
-210 + 24x + 26x2 + 2x3 + -2x3 = 2x2 + 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
-210 + 24x + 26x2 + 0 = 2x2 + 2x3 + -2x3
-210 + 24x + 26x2 = 2x2 + 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
-210 + 24x + 26x2 = 2x2 + 0
-210 + 24x + 26x2 = 2x2

Solving
-210 + 24x + 26x2 = 2x2

Solving for variable 'x'.

Combine like terms: 26x2 + -2x2 = 24x2
-210 + 24x + 24x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-210 + 24x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-35 + 4x + 4x2) = 0

Factor a trinomial.
6((-7 + -2x)(5 + -2x)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-7 + -2x)' equal to zero and attempt to solve: Simplifying -7 + -2x = 0 Solving -7 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x = 0 + 7 -2x = 0 + 7 Combine like terms: 0 + 7 = 7 -2x = 7 Divide each side by '-2'. x = -3.5 Simplifying x = -3.5

Subproblem 2

Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {-3.5, 2.5}

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