4x^2-29x+30=-6x^2+10-59x

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Solution for 4x^2-29x+30=-6x^2+10-59x equation: 


Simplifying
4x2 + -29x + 30 = -6x2 + 10 + -59x

Reorder the terms:
30 + -29x + 4x2 = -6x2 + 10 + -59x

Reorder the terms:
30 + -29x + 4x2 = 10 + -59x + -6x2

Solving
30 + -29x + 4x2 = 10 + -59x + -6x2

Solving for variable 'x'.

Reorder the terms:
30 + -10 + -29x + 59x + 4x2 + 6x2 = 10 + -59x + -6x2 + -10 + 59x + 6x2

Combine like terms: 30 + -10 = 20
20 + -29x + 59x + 4x2 + 6x2 = 10 + -59x + -6x2 + -10 + 59x + 6x2

Combine like terms: -29x + 59x = 30x
20 + 30x + 4x2 + 6x2 = 10 + -59x + -6x2 + -10 + 59x + 6x2

Combine like terms: 4x2 + 6x2 = 10x2
20 + 30x + 10x2 = 10 + -59x + -6x2 + -10 + 59x + 6x2

Reorder the terms:
20 + 30x + 10x2 = 10 + -10 + -59x + 59x + -6x2 + 6x2

Combine like terms: 10 + -10 = 0
20 + 30x + 10x2 = 0 + -59x + 59x + -6x2 + 6x2
20 + 30x + 10x2 = -59x + 59x + -6x2 + 6x2

Combine like terms: -59x + 59x = 0
20 + 30x + 10x2 = 0 + -6x2 + 6x2
20 + 30x + 10x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
20 + 30x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(2 + 3x + x2) = 0

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

Ignore the factor 10.

Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-2, -1}

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